A study of strongly Cohen-Macaulay ideals by delta invariant

Abstract

Let $R$ be a Cohen-Macaulay local ring, $I$ a strongly Cohen-Macaulay ideal of $R$. We show that $R/{\mathrm{Ann}}_R(I)$ is a maximal Cohen-Macaulay $R$-module by means of the delta-invariant. Also it is shown that there exists a Cohen-Macaulay ideal $J$ of $R$ such that the ${\delta }_{R/J}$-invariant of all Koszul homologies of $R$ with respect $I$ is zero.

7 pages; final version; to appear in Bulletin of the Iranian Mathematical Society