# Cohen-Macaulayness of trivial extensions

## TL;DR

This paper investigates conditions under which trivial extensions of commutative rings by modules are Cohen-Macaulay, extending the concept of Cohen-Macaulayness from rings to modules for a broader understanding.

## Contribution

It introduces a generalized notion of Cohen-Macaulayness applicable to modules and characterizes when trivial extensions possess this property.

## Key findings

- Provides criteria for Cohen-Macaulayness of trivial extensions
- Extends Cohen-Macaulay theory from rings to modules
- Offers new insights into the structure of trivial extensions

## Abstract

Our goal is to determine when the trivial extensions of commutative rings by modules are Cohen-Macaulay in the sense of Hamilton and Marley. For this purpose, we provide a generalization of the concept of Cohen-Macaulayness of rings to modules.