Cohen-Macaulayness with respect to Serre classes

TL;DR

This paper introduces a new concept of regular sequences relative to Serre classes in commutative Noetherian rings and develops a theory of Cohen-Macaulayness based on this framework.

Contribution

It defines regular sequences with respect to Serre classes and extends Cohen-Macaulay theory to this context, providing foundational properties.

Findings

Regular sequences with respect to Serre classes are characterized.

A theory of Cohen-Macaulayness relative to Serre classes is established.

Key properties of these new notions are demonstrated.

Abstract

Let $R$ be a commutative Noetherian ring. The notion of regular sequences with respect to a Serre class of $R$-modules is introduced and some of their essential properties are given. Then in the local case, we explore a theory of Cohen-Macaulayness with respect to Serre classes.