Term of Award

Fall 2011

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Alina C. Iacob

Committee Member 1

David R. Stone

Committee Member 2

Andrew V. Sills

Abstract

Purpose: H. Holm's metatheorem states, "Every result in classical homological algebra has a counterpart in Gorenstein homological algebra". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of a famous theorem of Gruson, Jensen, and Raynaud. Using this result we prove that over such rings, a module M having finite Gorenstein at dimension is equivalent to M having finite Gorenstein projective dimension.

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