Relative Cohen-Macaulay modules under ring homomorphisms

TL;DR

This paper investigates how certain classes of relative Cohen-Macaulay modules behave under specific types of ring homomorphisms, extending existing results in homological algebra.

Contribution

It introduces new invariance properties of relative Cohen-Macaulay modules under pure and finite flat dimension ring homomorphisms.

Findings

Invariance of relative Cohen-Macaulay modules under pure ring homomorphisms

Extension of known results to ring homomorphisms of finite flat dimension

Broader understanding of homological module behavior under ring maps

Abstract

Let $R$ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a$ a proper ideal of $R$. We study the invariance of some classes of $\frak a$-relative Cohen-Macaulay modules under pure ring homomorphisms and ring homomorphisms of finite flat dimension. Our results extend several results in the existing literature on homological modules.