On Gorenstein Projective and Gorenstein Flat Modules

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.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2011

Author dc:creator

• Smith, Chasen Grady

Contributors dc:contributor

• David R. Stone
• Andrew V. Sills

• ETD
• Module
• Projective
• Injective
• Flat
• Krull dimension
• Noetherian
• Gorenstein

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/673

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1673