Decomposition of Modules and Tensor Products over Principal Subalgebras of Truncated Polynomial Rings

Author

Kevin Steine Jr. Harris

ORCID Identifier(s)

0000-0003-0053-1824

Graduation Semester and Year

2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

David A Jorgensen

Abstract

The topic of my dissertation is to investigate the behavior of modules and tensor products over a truncated polynomial ring with prime characteristic. This investigation utilizes principal subalgebras of the truncated polynomial ring as the main tool for studying these objects. Then, we investigate if these modules and their tensor products have a similar behavior when viewed over more general truncated polynomial rings. In particular, we aim to investigate the behavior of these objects when we replace principal subalgebras over a field with prime characteristic by hypersurfaces over a field with no characteristic restriction.

Keywords

Truncated polynomial rings, Tensor products, Prime characteristic

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

Harris, Kevin Steine Jr., "Decomposition of Modules and Tensor Products over Principal Subalgebras of Truncated Polynomial Rings" (2022). Mathematics Dissertations. 198.
https://mavmatrix.uta.edu/math_dissertations/198