# Properties of modules with zero delta invariant

Research paper by Mohammad T. Dibaei, Yaser Khalatpour

Indexed on: 11 Nov '18Published on: 11 Nov '18Published in: arXiv - Mathematics - Commutative Algebra

#### Abstract

Let $R$ be a Cohen-Macaulay local ring, $I$ a strongly Cohen-Macaulay ideal of $R$. 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. Also we show that $R/0:_R I$ is a maximal Cohen-Macaulay $R$-module by means of the delta-invariant, which improves a result due to Craig Huneke.