almost Cohen-Macaulayness of Koszul homology
Bull. Korean Math. Soc.
Published online 2019 Mar 12
Amir Mafi, and Samaneh Tabejamaat
Payame Noor University, University of Kurdistan
Abstract : ‎Let $(R,\frak{m})$ be a commutative Noetherian ring‎, ‎$I$ an ideal of $R$ and $M$ a non-zero finitely generated $R$-module‎. ‎We show that if $M$ and $H_0(I,M)$ are aCM $R$-modules and $I=(x_1,...,x_{n+1})$ such that $x_1,...,x_n$ is an $M$-regular sequence‎, ‎then $H_i(I,M)$ is an aCM $R$-module for all $i$‎.
‎Moreover‎, ‎we prove that if $R$ and $H_i(I,R)$ are aCM for all $i$‎, ‎then $R/(0:I)$ is aCM‎. ‎In addition‎, ‎we prove that if $R$ is‎
‎aCM and $x_1,...,x_n$ is an aCM $d$-sequence‎, ‎then $\depth H_i(x_1,...,x_n;R)\geq i-1$ for all $i$‎.
Keywords : Almost Cohen-Macaulay modules‎, ‎Koszul homology
MSC numbers : 13C14,13D07
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