UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (4/20/2007) at 5:00 pm in 487 Pickard Hall

Speaker: William Purpura
AmeriCredit, Fort Worth, Texas

"Gorenstein Dimension"

Abstract: In this talk we present the fundamentals of Gorenstein dimension introduced by Auslander and Bridger in 1969. The Gorenstein dimension of a module M (written Gd-M) is obtained by resolving M by totally reflexive modules. Over a local ring (R,m), the class of totally reflexive modules contains the class of projectives. The Gorenstein dimension has some very nice properties, one of which is Gd-M<=pd M with equality holding when pd M is finite. Another is a refinement of the much famed Auslander-Buchsbaum Theorem. These results as well as some examples of totally reflexive modules will be presented.