# Notes on linkage of modules

## TL;DR

This paper investigates how the Cohen-Macaulay property is preserved under linkage in local rings and explores the relationship between linked modules' properties and local cohomology.

## Contribution

It demonstrates conditions under which Cohen-Macaulayness is preserved under linkage and analyzes the connection between (S_n) loci and local cohomology attached primes.

## Key findings

- Cohen-Macaulayness is preserved under linkage under mild conditions.
- The (S_n) locus of linked modules relates to attached primes of local cohomology.
- Provides new insights into the structure of linked modules in Cohen-Macaulay rings.

## Abstract

Let R be a Cohen-Macaulay local ring. It is shown that under some mild conditions, the Cohen-Macaulayness property is preserved under linkage. We also study the connection of (S_n) locus of a horizontally linked module and the attached primes of certain local cohomology modules of its linked module.