Graduation Semester and Year

2009

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

David A Jorgensen

Abstract

In this paper, we discuss conditions for uniqueness among minimal acyclic complexes of finitely generated free modules over a commutative local ring which share a common syzygy module. Although such uniqueness occurs over Gorenstein rings, the question has been asked whether two minimal acyclic complexes in general can be isomorphic to the left and non-isomorphic to the right. We answer the question in the negative for certain cases, including periodic complexes, sesqui-acyclic complexes, and certain rings with radical cube zero. In particular, we investigate the question for graded algebras with Hilbert series $H_R(t)=1+et+(e-1)t^2$, and such monomial algebras possessing a special generator.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

Share

COinS