Bryan White

Publication Date

7-12-2014

Abstract

We aim to classify the star and semistar operations on conductive numerical semigroup rings which are of the form $k + x^n k[[x]]$. By classifying the star and semistar operations on conductive numerical semigroup rings we obtain a better understanding of the set of star and semistar operations on general numerical semigroup rings. Here we classify all star and semistar operations on the ring $ k + x^4 k[[x]]$ as well as all semistar operations on $k+x^5k[[x]]$ that are not star. We investigate star operations on $k+x^5k[[x]]$ with Macaulay 2 and also present several results about general conductive numerical semigroup rings that bring us closer to our goal.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Janet Vassilev

Second Committee Member

Alexandru Buium

Third Committee Member

Michael Nakamaye

Fourth Committee Member

Bruce Olberding

Language

English

Keywords

Commutative Algebra, Numerical Semigroup, Star Operation

Document Type

Dissertation

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