Gorenstein Homological Modules And Dimensions Over Triangular Matrix Rings

The topics of this paper are Gorenstein homological modules and dimensions over triangular matrix rings. First of all, we character the Gorenstein homological dimensions of modules over triangular matrix rings, and discuss when a module over triangular matrix ring is Gorenstein flat module. Especially, it is investigated that when the triangular matrix ring of order n is left Gorenstein regular. Then we ob-tain a necessary and sufficient condition for a left module to be strongly Gorenstein homological modules over triangular matrix rings. At last, the methods of con-structing Gorenstein projective, flat (pre)covers and Gorenstein injective, cotorsion (pre)envelopes of the modules over triangular matrix rings are given.