ORCID Identifier(s)

0009-0004-1749-1763

Graduation Semester and Year

2023

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

David Jorgensen

Abstract

We are interested in quantitative information on the freeness of modules over a truncated polynomial ring when restricting to subalgebras generated by a linear form. After investigating the structure of the truncated polynomial ring, subalgebras generated by a linear form, and corresponding vector spaces, we construct a generic representation and discuss its connection to a certain affine space. We quantify the abundance of freeness of modules using a certain variety called the rank variety. For any possible dimension we construct a module whose rank variety has that dimension. Finally, we define another variety, called the module variety, and show that the dimension of this variety is invariant under a change of subalgebra.

Keywords

Commutative Algebra, Anp-Module

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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