Construction of Gorenstein projective modules over tensor rings

TL;DR

This paper characterizes Gorenstein projective modules over tensor rings, providing conditions and methods to construct such modules from base rings, with applications to various ring extensions.

Contribution

It offers a comprehensive framework for understanding and constructing Gorenstein projective modules over tensor rings, extending previous theories.

Findings

Characterization of Gorenstein projective modules over tensor rings

Method to construct Gorenstein projective modules from base rings

Applications to trivial ring extensions, Morita rings, and triangular matrix rings

Abstract

For a tensor ring $T_R(M)$, we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective modules over $T_R(M)$ from the ones of $R$. Some applications to trivial ring extensions, Morita context rings and triangular matrix rings are given.