The Gorenstein-projective Modules Over Some Upper Triangular Matrix Artin Algebras

In Gorenstein homological algebra, the basic notions, such as free (resp. projective, in-jective, and flat) modules, are the strong Gorenstein-projective (resp. Gorenstein-projective, Gorenstein-injective, and Gorenstein-flat) modules. The relative homological algebra, espe-cially the Gorenstein homological algebra, has been developed to an advanced level. But up to now, there are no efficient ways of constructing concretely (especially finitely generated) Gorenstein-projective modules. In this paper, a new class of algebras TRn(A) is introduced, their module categories are described. We get the following results:TRn(A) is a Goren-stein algebra if and only if so is A, and all the Gorenstein-projective TRn(A)-modules are explicitly determined when TRn(A) is Gorenstein.