# $I$-Cohen Macaulay modules

## TL;DR

This paper introduces and studies the properties of $I$-Cohen Macaulay modules, a generalization of Cohen Macaulay modules, revealing their structure and providing various characterizations.

## Contribution

It defines $I$-Cohen Macaulay modules and explores their properties, establishing analogies with Cohen Macaulay modules and offering new characterizations.

## Key findings

- $I$-Cohen Macaulay modules share properties with Cohen Macaulay modules.
- The paper provides multiple characterizations of $I$-Cohen Macaulay modules.
- Structural insights into $I$-Cohen Macaulay modules are presented.

## Abstract

A finitely generated module $M$ over a commutative Noetherian ring $R$ is called an $I$-Cohen Macaulay module, if \[ \grade(I,M) + \dim(M/IM)= \dim(M), \] where $I$ is a proper ideal of $R$. The aim of this paper is to study the structure of this class of modules. It is discovered that $I$-Cohen Macaulay modules enjoy many interesting properties which are analogous to those of Cohen Macaulay modules. Also, various characterizations of $I$-Cohen Macaulay modules are presented here.