Inverse matrix gamma distribution - Revision history

en>Gadget850: /* References */refbegin, replaced:
→ {{reflist}} using AWB

2014-12-31T11:27:56Z

References: refbegin, replaced: <div class="references-small"><references/></div> → {{reflist}} using AWB

← Older revision		Revision as of 13:27, 31 December 2014
Line 1:		Line 1:
	~~In [[abstract algebra]], '''Jacobson's conjecture''' is an open problem in [[ring theory]] concerning the intersection of powers of the [[Jacobson radical]] of a [[Noetherian ring]]~~.		I like Creative writing. <br>I also try to learn French in my free time.<br><br>Feel free to surf to my webpage :: [http://en.wikipedia.org/wiki/.gw gw timeshare services]

	~~It has only been proven for special types of Noetherian rings, so far. Examples exist~~ to ~~show that the conjecture can fail when the ring is not Noetherian on a side, so it is absolutely necessary for the ring to be two-sided Noetherian.~~

	~~The conjecture is named for the algebraist [[Nathan Jacobson]] who posed the first version of the conjecture~~.

	~~==Statement==~~
	~~For a ring ''R'' with Jacobson radical ''J'', the nonnegative powers ''J''~~<~~sup~~>~~''n''~~<~~/sup~~> ~~are defined by using the [[product of ideals]].~~

	:~~''Jacobson's conjecture~~:~~'' In a right-and-left~~ [~~[Noetherian ring]], <math>\bigcap_{n\in \mathbb{N}}J^n=\{0\}.</math>~~

	~~In other words~~: ~~"The only element of a Noetherian ring in all powers of ''J'' is 0."~~

	~~The original conjecture posed by Jacobson in 1956<ref>{{citation~~
	~~\| last = Jacobson \| first = Nathan~~
	~~\| location = 190 Hope Street, Prov., R. I.~~
	~~\| mr = 0081264~~
	~~\| page = 200~~
	~~\| publisher = American Mathematical Society~~
	~~\| series = American Mathematical Society, Colloquium Publications, vol. 37~~
	~~\| title = Structure of rings~~
	~~\| year = 1956}}. As cited by {{citation~~
	~~\| last1 = Brown \| first1 = K. A.~~
	~~\| last2 = Lenagan \| first2 = T. H.~~
	~~\| doi = 10.1017~~/~~S0017089500004729~~
	~~\| issue = 1~~
	~~\| journal = Glasgow Mathematical Journal~~
	~~\| mr = 641612~~
	~~\| pages = 7–8~~
	~~\| title = A note on Jacobson's conjecture for right Noetherian rings~~
	~~\| volume = 23~~
	~~\| year = 1982}}.<~~/ref> asked about noncommutative one-sided Noetherian rings, however [[Herstein]] produced a counterexample in 1965{{sfn\|Herstein\|1965}} and soon after Jategaonkar produced a different example which was a left [[principal ideal domain]].~~{{sfn\|Jategaonkar\|1968}} From that point on, the conjecture was reformulated to require two-sided Noetherian rings~~.

	~~==Partial results==~~
	~~Jacobson's conjecture has been verified for particular types of Noetherian rings:~~
	* [[commutative ring\|Commutative]] Noetherian rings all satisfy Jacobson's conjecture. This is a consequence of the [[Krull intersection theorem]].
	* [[Fully bounded Noetherian ring]]s{{sfn\|Cauchon\|1974}}{{sfn\|Jategaonkar\|1974}}
	* Noetherian rings with [[Krull dimension]] 1{{sfn\|Lenagan\|1977}}
	* Noetherian rings satisfying the [[second layer condition]]{{sfn\|Jategaonkar\|1982}}

	~~==References==~~
	~~{{Reflist}}~~
	*{{citation \|last=Cauchon\|first=Gérard \|title=Sur l'intersection des puissances du radical d'un T-anneau noethérien \|language=French \|journal=C. R. Acad. Sci. Paris Sér. A \|volume=279 \|year=1974 \|pages=91–93 \|mr=0347894}}
	*{{citation \|last1=Goodearl\|first1=K. R. \|last2=Warfield\|first2=R. B., Jr. \|title=An introduction to noncommutative Noetherian rings \|series=London Mathematical Society Student Texts \|volume=61 \|edition=2 \|publisher=Cambridge University Press \|place=Cambridge \|year=2004 \|pages=xxiv+344 \|isbn=0-521-83687-5 \|isbn=0-521-54537-4 \|mr=2080008 }}
	*{{citation \|last=Herstein \|first=I. N. \|title=A counterexample in Noetherian rings \|journal=Proc. Nat. Acad. Sci. U.S.A. \|volume=54 \|year=1965 \|pages=1036–1037 \|issn=0027-8424 \|mr=0188253}}
	*{{citation \|last=Jategaonkar \|first=Arun Vinayak \|title=Left principal ideal domains \|journal=J. Algebra \|volume=8 \|year=1968 \|pages=148–155 \|issn=0021-8693 \|mr=0218387}}
	*{{citation\|last=Jategaonkar \|first=Arun Vinayak \|title=Jacobson's conjecture and modules over fully bounded Noetherian rings \|journal=J. Algebra \|volume=30 \|year=1974 \|pages=103–121 \|issn=0021-8693 \|mr=0352170}}
	*{{citation \|last=Jategaonkar\|first=Arun Vinayak \|title=Solvable Lie algebras, polycyclic-by-finite groups and bimodule Krull dimension \|journal=Comm. Algebra\|volume=10 \|year=1982 \|number=1 \|pages=19–69 \|issn=0092-7872 \|mr=674687 \|doi=10.1080/~~00927878208822700}}~~
	*{{citation \|last=Lenagan\|first=T. H. \|title=Noetherian rings with Krull dimension one \|journal=J. London Math. Soc. ~~(2) \|volume=15 \|year=1977 \|number=1 \|pages=41–47 \|issn=0024-6107 \|mr=0442008}}~~
	*{{citation \|last=Rowen \|first=Louis H. \|title=Ring theory. Vol. I \|series=Pure and Applied Mathematics \|volume=127 \|publisher=Academic Press Inc. \|place=Boston, MA \|year=1988 \|pages=xxiv+538 \|isbn=0-12-599841-4 \|mr=940245}}

	~~[[Category:Conjectures\| ]]~~
	~~[[Category:Ring theory]~~]

en>Shorespirit: added missing symbol, fixed reference format

2013-12-26T20:40:04Z

added missing symbol, fixed reference format

← Older revision		Revision as of 22:40, 26 December 2013
Line 1:		Line 1:
			In [[abstract algebra]], '''Jacobson's conjecture''' is an open problem in [[ring theory]] concerning the intersection of powers of the [[Jacobson radical]] of a [[Noetherian ring]].

			It has only been proven for special types of Noetherian rings, so far. Examples exist to show that the conjecture can fail when the ring is not Noetherian on a side, so it is absolutely necessary for the ring to be two-sided Noetherian.

	~~, forgetful owner, no more interest in site, no longer in business, no longer active or didn't pay~~ for ~~whatever reason). Good domain names create good impression of~~ the ~~website that allows one to succeed. Even a resident~~ of ~~Canada or~~ the ~~company, organization which has its presence in Canada can proceed with the task~~. ~~What~~ a ~~great feeling it is getting~~ '~~reward points~~' ~~for going into debt. This means that you will have to make your primary keyword the same as your domaine name. A hosted PBX system~~ with ~~all its powerful telecommunication features attracts more customers to your business~~, ~~improves productivity and brings in more revenue for your business. Read about~~ the ~~opinions of other people on~~ the product. <br><br>~~Browser based, it works with any operating system and allows secure video facilities for~~ all ~~who need them (check if available~~ in ~~your~~ location, ~~as the facility is not offered in all countries)~~. ~~If you have multiple websites for your company for each of your products and services~~, ~~you may speak to your hosting provider and migrate your site to a multiple domain hosting account~~. ~~Not only are these domains cheap but there are also a few good [https://Www~~.~~Google.com/search?hl~~=~~en&gl~~=~~us&tbm~~=~~nws&q~~=dictionary&btnI=lucky dictionary] names available for the. The good news is there has never been a better time to start a business from home because the Internet makes it a low-cost and low-risk venture. Even though, ~~these kinds extension cords can exactly relate to what kind of business you could have~~, ~~however if possible if you are able to give it, you can get for plug-ins in addition to~~. ~~Providers also can help you cater to the needs~~ of ~~your customers and boost your sales with the e-commerce solutions that are equally affordable. If you need a cheap domain with huge space to store emails then it might be costlier~~. ~~<br><br>As you have decided to create your own website, you defiantly need a reputable web host who can provide you space within reasonable prices~~. ~~There isn't a great deal to navigate through either because this phone has a very limited feature set~~. Comparative studies with archaea have enabled greater elucidation of evolutionary history, and with multiple enzymes that are stable at high temperatures, the microbes have practical application in medicine, food science, and other industries. ~~Be sure that you are the license holder of the cheap domain names~~. ~~However, most of the times, when people think of creating a site, they try to save costs and choose the cheapest domain names that are available from cheap domain name registration companies~~. A ~~brand having a respected brand name can generate revenue. There are certain ways you can earn from these names actually but that~~'s ~~a different issue~~. <br>~~<br>But~~, ~~not all cheap~~ domain ~~hosting companies are the same. Select the Also Delete Your Browsing Data check box~~. ~~The strategies are considered dynamic and are responsive to the ongoing data analysis of your SEO performance~~ that ~~you should be collecting and reviewing~~ on ~~a regular basis. Well of course by now you have figured out that this article really~~ was ~~meant~~ to ~~be a joke~~. ~~com~~ been ~~providing a vpn~~'s ~~to gain freedom on the internet~~. ~~Quick Cooling - We have done this and it feels great. You need to choose your domain name with great care so that as it~~ is ~~representative~~ of ~~who you are and what your business stands for~~. ~~<br><br>Historical evidence shows that international domain name set up was an outcome to fulfill~~ the ~~requirement for internationalized domain names containing non~~-~~ASCII characters~~. ~~With so many web sites on the internet already, many of the good domain names have been taken~~. ~~Lots of online entrepreneurs make this mistake: they can't separate their private lives from their business lives~~. ~~' One after the other, visit the website of each product to gain an idea of it as regards its benefits and features~~. ~~I am sure you would agree there is nothing wrong with that considering they are paying you for your work so what do you care what they do with it afterward~~. ~~We realize the trouble involved in this and hence provide you appropriate assistance on setting up your web sites~~. ~~You must be aware of Go - Daddy coupons~~, ~~as this renowned hosting service provider offers various affordable rate domain and web hosting services~~. ~~<br><br>Most of the times there is some catch or the other when a domain name registration company offers a domain name at a cheap cost~~. ~~Domains are registered with the Domain Name Registrar~~. ~~If you are new and have no idea about all this then you must stay careful as you might land yourself into troubles~~. ~~As long as you run your website on their servers, you get a free domain name for life~~. ~~Buying cheap domains is not at all a tough job; there are several providers who host website and provide [http://www~~.~~cheapdomains~~.~~com/ cheap domains]~~. ~~This can be of great help as people today spend millions on getting higher ranks~~. ~~The Affective Domain will be broken down within these paragraphs~~. ~~<br><br>If you asked this person after he got his i~~ - ~~Pad if it was worth it, I can guarantee they would say NO~~. ~~Publish the article to a few article directories (most are free)~~ and ~~the search engine spiders that crawl websites looking for new~~ pages ~~will soon pick up the hyperlink to your new site~~, ~~go to your site~~ and ~~index all the~~ pages ~~it can find from there~~. ~~Normally the standard features of a site will include these features~~. ~~After you in the end decide witch website hosting company you are going to register~~ with ~~be convinced it meets with in your budget~~. ~~Level five, and final level, is naturalization which is taking the actions from the conscious to the subconscious~~. ~~The website owner gets the benefit of free hosting~~ and ~~the experts of the company will also help them with their domain look up~~. ~~Anyway~~, ~~you get the power and functionality can not be compared.~~		The conjecture is named for the algebraist [[Nathan Jacobson]] who posed the first version of the conjecture.

			==Statement==
			For a ring ''R'' with Jacobson radical ''J'', the nonnegative powers ''J''<sup>''n''</sup> are defined by using the [[product of ideals]].

			:''Jacobson's conjecture:'' In a right-and-left [[Noetherian ring]], <math>\bigcap_{n\in \mathbb{N}}J^n=\{0\}.</math>

			In other words: "The only element of a Noetherian ring in all powers of ''J'' is 0."

			The original conjecture posed by Jacobson in 1956<ref>{{citation
			\| last = Jacobson \| first = Nathan
			\| location = 190 Hope Street, Prov., R. I.
			\| mr = 0081264
			\| page = 200
			\| publisher = American Mathematical Society
			\| series = American Mathematical Society, Colloquium Publications, vol. 37
			\| title = Structure of rings
			\| year = 1956}}. As cited by {{citation
			\| last1 = Brown \| first1 = K. A.
			\| last2 = Lenagan \| first2 = T. H.
			\| doi = 10.1017/S0017089500004729
			\| issue = 1
			\| journal = Glasgow Mathematical Journal
			\| mr = 641612
			\| pages = 7–8
			\| title = A note on Jacobson's conjecture for right Noetherian rings
			\| volume = 23
			\| year = 1982}}.</ref> asked about noncommutative one-sided Noetherian rings, however [[Herstein]] produced a counterexample in 1965{{sfn\|Herstein\|1965}} and soon after Jategaonkar produced a different example which was a left [[principal ideal domain]].{{sfn\|Jategaonkar\|1968}} From that point on, the conjecture was reformulated to require two-sided Noetherian rings.

			==Partial results==
			Jacobson's conjecture has been verified for particular types of Noetherian rings:
			* [[commutative ring\|Commutative]] Noetherian rings all satisfy Jacobson's conjecture. This is a consequence of the [[Krull intersection theorem]].
			* [[Fully bounded Noetherian ring]]s{{sfn\|Cauchon\|1974}}{{sfn\|Jategaonkar\|1974}}
			* Noetherian rings with [[Krull dimension]] 1{{sfn\|Lenagan\|1977}}
			* Noetherian rings satisfying the [[second layer condition]]{{sfn\|Jategaonkar\|1982}}

			==References==
			{{Reflist}}
			*{{citation \|last=Cauchon\|first=Gérard \|title=Sur l'intersection des puissances du radical d'un T-anneau noethérien \|language=French \|journal=C. R. Acad. Sci. Paris Sér. A \|volume=279 \|year=1974 \|pages=91–93 \|mr=0347894}}
			*{{citation \|last1=Goodearl\|first1=K. R. \|last2=Warfield\|first2=R. B., Jr. \|title=An introduction to noncommutative Noetherian rings \|series=London Mathematical Society Student Texts \|volume=61 \|edition=2 \|publisher=Cambridge University Press \|place=Cambridge \|year=2004 \|pages=xxiv+344 \|isbn=0-521-83687-5 \|isbn=0-521-54537-4 \|mr=2080008 }}
			*{{citation \|last=Herstein \|first=I. N. \|title=A counterexample in Noetherian rings \|journal=Proc. Nat. Acad. Sci. U.S.A. \|volume=54 \|year=1965 \|pages=1036–1037 \|issn=0027-8424 \|mr=0188253}}
			*{{citation \|last=Jategaonkar \|first=Arun Vinayak \|title=Left principal ideal domains \|journal=J. Algebra \|volume=8 \|year=1968 \|pages=148–155 \|issn=0021-8693 \|mr=0218387}}
			*{{citation\|last=Jategaonkar \|first=Arun Vinayak \|title=Jacobson's conjecture and modules over fully bounded Noetherian rings \|journal=J. Algebra \|volume=30 \|year=1974 \|pages=103–121 \|issn=0021-8693 \|mr=0352170}}
			*{{citation \|last=Jategaonkar\|first=Arun Vinayak \|title=Solvable Lie algebras, polycyclic-by-finite groups and bimodule Krull dimension \|journal=Comm. Algebra\|volume=10 \|year=1982 \|number=1 \|pages=19–69 \|issn=0092-7872 \|mr=674687 \|doi=10.1080/00927878208822700}}
			*{{citation \|last=Lenagan\|first=T. H. \|title=Noetherian rings with Krull dimension one \|journal=J. London Math. Soc. (2) \|volume=15 \|year=1977 \|number=1 \|pages=41–47 \|issn=0024-6107 \|mr=0442008}}
			*{{citation \|last=Rowen \|first=Louis H. \|title=Ring theory. Vol. I \|series=Pure and Applied Mathematics \|volume=127 \|publisher=Academic Press Inc. \|place=Boston, MA \|year=1988 \|pages=xxiv+538 \|isbn=0-12-599841-4 \|mr=940245}}

			[[Category:Conjectures\| ]]
			[[Category:Ring theory]]

en>AnomieBOT: Dating maintenance tags: {{Cn}}

2012-05-22T23:22:46Z

Dating maintenance tags: {{Cn}}

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, forgetful owner, no more interest in site, no longer in business, no longer active or didn't pay for whatever reason). Good domain names create good impression of the website that allows one to succeed. Even a resident of Canada or the company, organization which has its presence in Canada can proceed with the task. What a great feeling it is getting 'reward points' for going into debt. This means that you will have to make your primary keyword the same as your domaine name. A hosted PBX system with all its powerful telecommunication features attracts more customers to your business, improves productivity and brings in more revenue for your business. Read about the opinions of other people on the product. Browser based, it works with any operating system and allows secure video facilities for all who need them (check if available in your location, as the facility is not offered in all countries). If you have multiple websites for your company for each of your products and services, you may speak to your hosting provider and migrate your site to a multiple domain hosting account. Not only are these domains cheap but there are also a few good [https://Www.Google.com/search?hl=en&gl=us&tbm=nws&q=dictionary&btnI=lucky dictionary] names available for the. The good news is there has never been a better time to start a business from home because the Internet makes it a low-cost and low-risk venture. Even though, these kinds extension cords can exactly relate to what kind of business you could have, however if possible if you are able to give it, you can get for plug-ins in addition to. Providers also can help you cater to the needs of your customers and boost your sales with the e-commerce solutions that are equally affordable. If you need a cheap domain with huge space to store emails then it might be costlier. As you have decided to create your own website, you defiantly need a reputable web host who can provide you space within reasonable prices. There isn't a great deal to navigate through either because this phone has a very limited feature set. Comparative studies with archaea have enabled greater elucidation of evolutionary history, and with multiple enzymes that are stable at high temperatures, the microbes have practical application in medicine, food science, and other industries. Be sure that you are the license holder of the cheap domain names. However, most of the times, when people think of creating a site, they try to save costs and choose the cheapest domain names that are available from cheap domain name registration companies. A brand having a respected brand name can generate revenue. There are certain ways you can earn from these names actually but that's a different issue. But, not all cheap domain hosting companies are the same. Select the Also Delete Your Browsing Data check box. The strategies are considered dynamic and are responsive to the ongoing data analysis of your SEO performance that you should be collecting and reviewing on a regular basis. Well of course by now you have figured out that this article really was meant to be a joke. com been providing a vpn's to gain freedom on the internet. Quick Cooling - We have done this and it feels great. You need to choose your domain name with great care so that as it is representative of who you are and what your business stands for. Historical evidence shows that international domain name set up was an outcome to fulfill the requirement for internationalized domain names containing non-ASCII characters. With so many web sites on the internet already, many of the good domain names have been taken. Lots of online entrepreneurs make this mistake: they can't separate their private lives from their business lives. ' One after the other, visit the website of each product to gain an idea of it as regards its benefits and features. I am sure you would agree there is nothing wrong with that considering they are paying you for your work so what do you care what they do with it afterward. We realize the trouble involved in this and hence provide you appropriate assistance on setting up your web sites. You must be aware of Go - Daddy coupons, as this renowned hosting service provider offers various affordable rate domain and web hosting services. Most of the times there is some catch or the other when a domain name registration company offers a domain name at a cheap cost. Domains are registered with the Domain Name Registrar. If you are new and have no idea about all this then you must stay careful as you might land yourself into troubles. As long as you run your website on their servers, you get a free domain name for life. Buying cheap domains is not at all a tough job; there are several providers who host website and provide [http://www.cheapdomains.com/ cheap domains]. This can be of great help as people today spend millions on getting higher ranks. The Affective Domain will be broken down within these paragraphs. If you asked this person after he got his i - Pad if it was worth it, I can guarantee they would say NO. Publish the article to a few article directories (most are free) and the search engine spiders that crawl websites looking for new pages will soon pick up the hyperlink to your new site, go to your site and index all the pages it can find from there. Normally the standard features of a site will include these features. After you in the end decide witch website hosting company you are going to register with be convinced it meets with in your budget. Level five, and final level, is naturalization which is taking the actions from the conscious to the subconscious. The website owner gets the benefit of free hosting and the experts of the company will also help them with their domain look up. Anyway, you get the power and functionality can not be compared.

← Older revision		Revision as of 13:27, 31 December 2014
Line 1:		Line 1:
	~~In [[abstract algebra]], '''Jacobson's conjecture''' is an open problem in [[ring theory]] concerning the intersection of powers of the [[Jacobson radical]] of a [[Noetherian ring]]~~.		I like Creative writing. <br>I also try to learn French in my free time.<br><br>Feel free to surf to my webpage :: [http://en.wikipedia.org/wiki/.gw gw timeshare services]

	~~It has only been proven for special types of Noetherian rings, so far. Examples exist~~ to ~~show that the conjecture can fail when the ring is not Noetherian on a side, so it is absolutely necessary for the ring to be two-sided Noetherian.~~

	~~The conjecture is named for the algebraist [[Nathan Jacobson]] who posed the first version of the conjecture~~.

	~~==Statement==~~
	~~For a ring ''R'' with Jacobson radical ''J'', the nonnegative powers ''J''~~<~~sup~~>~~''n''~~<~~/sup~~> ~~are defined by using the [[product of ideals]].~~

	:~~''Jacobson's conjecture~~:~~'' In a right-and-left~~ [~~[Noetherian ring]], <math>\bigcap_{n\in \mathbb{N}}J^n=\{0\}.</math>~~

	~~In other words~~: ~~"The only element of a Noetherian ring in all powers of ''J'' is 0."~~

	~~The original conjecture posed by Jacobson in 1956<ref>{{citation~~
	~~\| last = Jacobson \| first = Nathan~~
	~~\| location = 190 Hope Street, Prov., R. I.~~
	~~\| mr = 0081264~~
	~~\| page = 200~~
	~~\| publisher = American Mathematical Society~~
	~~\| series = American Mathematical Society, Colloquium Publications, vol. 37~~
	~~\| title = Structure of rings~~
	~~\| year = 1956}}. As cited by {{citation~~
	~~\| last1 = Brown \| first1 = K. A.~~
	~~\| last2 = Lenagan \| first2 = T. H.~~
	~~\| doi = 10.1017~~/~~S0017089500004729~~
	~~\| issue = 1~~
	~~\| journal = Glasgow Mathematical Journal~~
	~~\| mr = 641612~~
	~~\| pages = 7–8~~
	~~\| title = A note on Jacobson's conjecture for right Noetherian rings~~
	~~\| volume = 23~~
	~~\| year = 1982}}.<~~/ref> asked about noncommutative one-sided Noetherian rings, however [[Herstein]] produced a counterexample in 1965{{sfn\|Herstein\|1965}} and soon after Jategaonkar produced a different example which was a left [[principal ideal domain]].~~{{sfn\|Jategaonkar\|1968}} From that point on, the conjecture was reformulated to require two-sided Noetherian rings~~.

	~~==Partial results==~~
	~~Jacobson's conjecture has been verified for particular types of Noetherian rings:~~
	* [[commutative ring\|Commutative]] Noetherian rings all satisfy Jacobson's conjecture. This is a consequence of the [[Krull intersection theorem]].
	* [[Fully bounded Noetherian ring]]s{{sfn\|Cauchon\|1974}}{{sfn\|Jategaonkar\|1974}}
	* Noetherian rings with [[Krull dimension]] 1{{sfn\|Lenagan\|1977}}
	* Noetherian rings satisfying the [[second layer condition]]{{sfn\|Jategaonkar\|1982}}

	~~==References==~~
	~~{{Reflist}}~~
	*{{citation \|last=Cauchon\|first=Gérard \|title=Sur l'intersection des puissances du radical d'un T-anneau noethérien \|language=French \|journal=C. R. Acad. Sci. Paris Sér. A \|volume=279 \|year=1974 \|pages=91–93 \|mr=0347894}}
	*{{citation \|last1=Goodearl\|first1=K. R. \|last2=Warfield\|first2=R. B., Jr. \|title=An introduction to noncommutative Noetherian rings \|series=London Mathematical Society Student Texts \|volume=61 \|edition=2 \|publisher=Cambridge University Press \|place=Cambridge \|year=2004 \|pages=xxiv+344 \|isbn=0-521-83687-5 \|isbn=0-521-54537-4 \|mr=2080008 }}
	*{{citation \|last=Herstein \|first=I. N. \|title=A counterexample in Noetherian rings \|journal=Proc. Nat. Acad. Sci. U.S.A. \|volume=54 \|year=1965 \|pages=1036–1037 \|issn=0027-8424 \|mr=0188253}}
	*{{citation \|last=Jategaonkar \|first=Arun Vinayak \|title=Left principal ideal domains \|journal=J. Algebra \|volume=8 \|year=1968 \|pages=148–155 \|issn=0021-8693 \|mr=0218387}}
	*{{citation\|last=Jategaonkar \|first=Arun Vinayak \|title=Jacobson's conjecture and modules over fully bounded Noetherian rings \|journal=J. Algebra \|volume=30 \|year=1974 \|pages=103–121 \|issn=0021-8693 \|mr=0352170}}
	*{{citation \|last=Jategaonkar\|first=Arun Vinayak \|title=Solvable Lie algebras, polycyclic-by-finite groups and bimodule Krull dimension \|journal=Comm. Algebra\|volume=10 \|year=1982 \|number=1 \|pages=19–69 \|issn=0092-7872 \|mr=674687 \|doi=10.1080/~~00927878208822700}}~~
	*{{citation \|last=Lenagan\|first=T. H. \|title=Noetherian rings with Krull dimension one \|journal=J. London Math. Soc. ~~(2) \|volume=15 \|year=1977 \|number=1 \|pages=41–47 \|issn=0024-6107 \|mr=0442008}}~~
	*{{citation \|last=Rowen \|first=Louis H. \|title=Ring theory. Vol. I \|series=Pure and Applied Mathematics \|volume=127 \|publisher=Academic Press Inc. \|place=Boston, MA \|year=1988 \|pages=xxiv+538 \|isbn=0-12-599841-4 \|mr=940245}}

	~~[[Category:Conjectures\| ]]~~
	~~[[Category:Ring theory]~~]

Inverse matrix gamma distribution - Revision history

en>Gadget850: /* References */refbegin, replaced: → {{reflist}} using AWB

en>Shorespirit: added missing symbol, fixed reference format

en>AnomieBOT: Dating maintenance tags: {{Cn}}

en>Gadget850: /* References */refbegin, replaced:
→ {{reflist}} using AWB