Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Department of Mathematical Sciences
Alina C. Iacob
Committee Member 1
David R. Stone
Committee Member 2
Andrew V. Sills
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.
Smith, Chasen Grady, "On Gorenstein Projective and Gorenstein Flat Modules" (2011). Electronic Theses & Dissertations. 673.