Definition 10.137.6. Let $R$ be a ring. Given integers $n \geq c \geq 0$ and $f_1, \ldots , f_ c \in R[x_1, \ldots , x_ n]$ we say

\[ S = R[x_1, \ldots , x_ n]/(f_1, \ldots , f_ c) \]

is a *standard smooth algebra over $R$* if the polynomial

\[ g = \det \left( \begin{matrix} \partial f_1/\partial x_1
& \partial f_2/\partial x_1
& \ldots
& \partial f_ c/\partial x_1
\\ \partial f_1/\partial x_2
& \partial f_2/\partial x_2
& \ldots
& \partial f_ c/\partial x_2
\\ \ldots
& \ldots
& \ldots
& \ldots
\\ \partial f_1/\partial x_ c
& \partial f_2/\partial x_ c
& \ldots
& \partial f_ c/\partial x_ c
\end{matrix} \right) \]

maps to an invertible element in $S$.

## Comments (5)

Comment #235 by Daniel Miller on

Comment #240 by Johan on

Comment #241 by Johan on

Comment #1845 by Peter Johnson on

Comment #1883 by Johan on