Gorenstein Modules Over Triangular Matrix Rings And Recollements Induced By Them

In the thesis we discuss Gorenstein modules over triangular matrix rings and recollements induced by them.In the first place,we describe Gorenstein projective(injective)modules and Ding projective modules over lower triangular matrix rings of order n,and obtain the related results of Gorenstein projective(injective)dimension over lower triangular matrix rings of order n.In the next place,by constructing six triangle functors among triangulated categories,we get a recollement of triangulated categories induced by Ding projective modules.In addition,we investigate level modules and absolutely clean modules over triangular matrix rings of order 2,some equivalent characterizations of Gorenstein AC-projective(injective)modules over triangular matrix rings of order 2 are given,and hence obtain a recollement of triangulated categories induced by Gorenstein AC-projective(injective)modules.