Coregular sequences and top local homology modules

Abstract

In this paper, we show that if $M$ is a non-zero Artinian $R$-module and $\underline{x}:=x_1,\ldots,x_n$ is an $M$-coregular sequence, then $x_1,\ldots,x_n$ is a $D(H_n^{\underline{x}}(M))$-coregular sequence. Moreover, if $R$ is complete with respect to $I$-adic topology and $d=\mathrm{Ndim} M$, then $\dim H^I_d(M) \le d$ and $\mathrm{depth} H_I^d(M)\ge \min\{{2, d}\}$ whenever $H^I_d(M) \ne 0.$