**Commutative Algebra Webinars**

Some Algebraic Properties of M/PM

Ahad Rahimi, Razi University

22 OCT 2020

11:00 - 13:00

Let k be a field, S = k[x1,..., xm, y1, ..., yn] a standard bigraded polynomial ring, and M a finitely generated bigraded S-module. We set P = (x1,..., xm) and Q = (y1,...,yn). In this talk, we will discuss several algebraic properties of M/PM, namely:

(a) If M is Cohen-Macaulay with respect to Q, then M/PM is Cohen-Macaulay.

(b) If M is sequentially Cohen-Macaulay with respect to Q, then M/PM is sequentially Cohen-Macaulay.

(c) If M is generalized Cohen-Macaulay with respect to Q, then M/PM is generalized Cohen-Macaulay.

Finally, if M has Maximal depth with respect to Q, then M/PM has no maximal depth in general.

To join the meeting, go to the following link:

https://vmeeting.ipm.ir/b/mat-9px-g3c