Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



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


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, . . .).

Included in

Algebra Commons