Term of Award
Fall 2011
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
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.
Recommended Citation
Smith, Chasen Grady, "On Gorenstein Projective and Gorenstein Flat Modules" (2011). Electronic Theses and Dissertations. 673.
https://digitalcommons.georgiasouthern.edu/etd/673
Research Data and Supplementary Material
No
