Gorenstein Projective Modules Over a Class of Generalized Matrix Algebras and their Applications

Abstract

In this article, we introduce a class of generalized matrix algebras, in which each algebra is called a normally upper triangular gm algebra, and characterise Gorenstein projective modules over this class of algebras. Moreover, a sufficient condition of strongly Gorenstein projective modules over normally upper triangular gm algebras is given. The importance of normally upper triangular gm algebras for us is that it includes the so-called path algebras of quivers over algebras and generalized path algebras. Due to this, we characterize Gorenstein projective modules and strongly Gorenstein projective modules over path algebras of quivers over algebras and generalized path algebras as applications of the main results on normally upper triangular gm algebras. At last, we give an example to show how all indecomposable Gorenstein projective modules over a given algebra are constructed by the result on generalized path algebras.