Gorenstein Projective Modules And Rings Of Finite Cohen-Macaulay Type

The topics of this thesis are Gorenstein projective modules and rings of fniteCohen-Macaulay type. The following are the main results.1. We describe all Gorenstein projective modules of a class of upper trian-gular matrix ring. We construct all Gorenstein injective modules of a class ofupper triangular matrix ring. We give an equivalent conditions of GorensteinT-modules of the T2-extension ring.2. We prove that R is Virtually Gorenstein ring if and only if so is itsT2-extension.3. We prove that a ring R is Gorenstein and Cohen-Macaulay fnite if andonly if there is a weakly resolving Gorenstein projective module E such that theglobe dimension of the endomorphism ring of E is fnite.When R is a Cohen-Macaulay fnite1-Gorenstein Artin algebra, we obtaina necessary and sufcient condition for the Cohen-Macaulay fniteness of its T2-extension. As an application, we give an example of Cohen-Macanlay fnite,representation infnite and globe dimension infnite Gorenstein algebrra.4. An equivalent description for a cotilting module with fnite left perpen-dicular category is obtained. Some applications this result are given in quasi-hereditary algebras and the representation of Artin algebras.