choosing generators $f_1, \ldots , f_ t$ for $J$ we have

the Jacobian ideal of $B$ over $A$, namely the ideal in $B$ generated by the $r \times r$ minors of the matrx $(\partial f_ j/\partial x_ i)_{1 \leq i \leq r, 1 \leq j \leq t}$, contains the ideal $I^ cB$ for some $c$, and

the Cramer ideal of $B$ over $A$, namely the ideal in $B$ generated by the image in $B$ of the $r$th Fitting ideal of $J$ as an $A[x_1, \ldots , x_ r]^\wedge $-module, contains $I^ cB$ for some $c$.

## Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)