Layer lengths, torsion theories and the finitistic dimension

TL;DR

This paper introduces a new measure called layer length, generalizing Loewy length, to analyze finitely generated modules over artinian rings using torsion theories.

Contribution

It proposes the concept of layer length associated with torsion theories, extending the classical Loewy length for modules over artinian rings.

Findings

Layer length provides a new way to measure modules.

The concept generalizes existing length measures.

Applications to finitistic dimension are discussed.

Abstract

Let $\Lambda$ be an artinian ring. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for finitely generated $\Lambda$-modules.