The Uniqueness Of Minimal Acyclic Complexes

Author

Meri Trema Hughes

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

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Hughes, Meri Trema, "The Uniqueness Of Minimal Acyclic Complexes" (2009). Mathematics Dissertations. 206.
https://mavmatrix.uta.edu/math_dissertations/206