Gorenstein Projective Modules over Triangular Matrix Rings

Abstract

Let R and S be Artin algebras and Γ be their triangular matrix extension via a bimodule SMR. We study totally acyclic complexes of projective Γ-modules and obtain a complete description of Gorenstein projective Γ-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras. © 2016 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.