Jacobian ideal

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

$J_f := \left\langle \frac{\partial f}{\partial x_1}, \ldots, \frac{\partial f}{\partial x_n} \right\rangle.$

See also

• Milnor number
• Unfolding