# On modules with reducible complexity

## TL;DR

This paper generalizes a depth equality in local rings using the concept of reducible complexity, expanding its application from group algebras to local algebra.

## Contribution

It extends previous results by incorporating the notion of reducible complexity, providing a broader understanding of depth properties in local algebra.

## Key findings

- Generalized a depth equality over local rings
- Utilized the concept of reducible complexity in the proof
- Connected ideas from group algebra modules to local algebra

## Abstract

In this paper we generalize a result, concerning a depth equality over local rings, proved independently by Araya and Yoshino, and Iyengar. Our result exploits complexity, a concept which was initially defined by Alperin for finitely generated modules over group algebras, introduced and studied in local algebra by Avramov, and subsequently further developed by Bergh.