College of Graduate Studies: Theses & Dissertations

Term of Award

Spring 2026

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Alina Iacob

Committee Member 1

Paul Sobaje

Committee Member 2

Yi Hu

Abstract

This thesis surveys known results on the existence of Gorenstein projective precovers and studies conditions under which the class of Gorenstein projective modules is precovering. In classical homological algebra, projective resolutions are used to study modules, while relative homological algebra replaces projective modules with a different class that must be precovering for resolutions to exist. Gorenstein homological algebra extends these ideas using Gorenstein projective modules. We review key developments by Jorgensen, Murfet and Salarian, Estrada, Iacob, and Yeomans, and Cortés and Saroch. We discuss the strongest known existence result, showing that Gorenstein projective precovers exist under suitable conditions; in particular, the best result so far is that the class GP is special precovering over right coherent left n-perfect rings. We also describe recent work reducing the problem to finitely presented modules.

OCLC Number

1588662513

Research Data and Supplementary Material

No

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