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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Flattery, Luke Manford, "A STUDY IN THE FREENESS OF FINITELY GENERATED Anp-MODULES UPON RESTRICTION TO PRINCIPAL SUBALGEBRAS" (2023). Mathematics Dissertations. 233.
https://mavmatrix.uta.edu/math_dissertations/233
Comments
Degree granted by The University of Texas at Arlington