Local algebras with radical cubic zero are PCM-free

TL;DR

This paper proves that local artin algebras with radical cubic zero have the property that all finitely generated Gorenstein projective modules with a projective submodule are necessarily projective, establishing a new class of PCM-free algebras.

Contribution

The paper demonstrates that artin local algebras with radical cubic zero are PCM-free, expanding understanding of Gorenstein projective modules in algebra.

Findings

Artin local algebras with radical cubic zero are PCM-free.

Gorenstein projective modules with a projective submodule are projective in this class.

Provides new insights into the structure of modules over specific algebra classes.

Abstract

An artin algebra is said to be PCM-free if every finitely generated Gorenstein projective module with a projective submodule is projective. In this paper, we show that artin local algebras with radical cubic zero are PCM-free.