Coregular sequences and top local homology modules

Authors : Nguyen Minh TRI

Pages : 38-48

Doi:10.24330/ieja.1058393

View : 14 | Download : 13

Publication Date : 2022-01-17

Article Type : Research Paper

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 $Dinsert ignore into journalissuearticles values(H_n^{\underline{x}}insert ignore into journalissuearticles values(M););$-coregular sequence. Moreover, if $R$ is complete with respect to $I$-adic topology and $d=\mathrm{Ndim} M$, then $\dim H^I_dinsert ignore into journalissuearticles values(M); \le d$ and $\mathrm{depth} H_I^dinsert ignore into journalissuearticles values(M);\ge \min\{{2, d}\}$ whenever $H^I_dinsert ignore into journalissuearticles values(M); \ne 0.$
Keywords : Coregular sequence, local homology, Co Cohen Macaulay module