Folkman's theorem

In mathematics the Jacobian ideal or gradient ideal is the ideal generated by the Jacobian of a function or function germ. Let $\mathcal{𝒪}(x_1,\dots ,x_n)$ denote the ring of smooth functions and f a function in the ring. The Jacobian ideal of f is

$J_f:=⟨\frac{\partial f}{\partial x_1},\dots ,\frac{\partial f}{\partial x_n}⟩.$

See also

• Milnor number
• Unfolding

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