Date on Master's Thesis/Doctoral Dissertation
8-2018
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
Degree Program
Applied and Industrial Mathematics, PhD
Committee Chair
Kulosman, Hamid
Committee Member
Hill, Aaron
Committee Member
Li, Jinjia
Committee Member
Seif, Steve
Committee Member
Brown, David N.
Author's Keywords
commutative algebra; integral domains; monoid domains; factorization
Abstract
We investigate the atomicity and the AP property of the semigroup rings F[X; M], where F is a field, X is a variable and M is a submonoid of the additive monoid of nonnegative rational numbers. In this endeavor, we introduce the following notions: essential generators of M and elements of height (0, 0, 0, . . .) within a cancellative torsion-free monoid Γ. By considering the latter, we are able to determine the irreducibility of certain binomials of the form Xπ − 1, where π is of height (0, 0, 0, . . .), in the monoid domain. Finally, we will consider relations between the following notions: M has the gcd/lcm property, F[X; M] is AP, and M has no elements of height (0, 0, 0, . . .).
Recommended Citation
Gipson, Ryan H., "Factorization in integral domains." (2018). Electronic Theses and Dissertations. Paper 3056.
https://doi.org/10.18297/etd/3056
