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.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Commutative Algebra, Numerical Semigroup, Star Operation
White, Bryan. "Star Operations and Numerical Semigroup Rings." (2014). https://digitalrepository.unm.edu/math_etds/55