Depth and Stanley depth of multigraded modules

TL;DR

This paper investigates how the algebraic invariants depth and Stanley depth change within short exact sequences of multigraded modules and when reducing modulo an element, providing insights into their behavior.

Contribution

It offers new theoretical results on the behavior of depth and Stanley depth in multigraded modules under exact sequences and reductions.

Findings

Characterization of depth behavior in short exact sequences

Analysis of Stanley depth variations under module reduction

New bounds and relations for depth and Stanley depth

Abstract

We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element.