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University of Louisville

1. Gipson, Ryan H. Factorization in integral domains.

Degree: PhD, 2018, University of Louisville

URL: 10.18297/etd/3056 ; https://ir.library.louisville.edu/etd/3056

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, . . .).
*Advisors/Committee Members: Kulosman, Hamid, Hill, Aaron, Hill, Aaron, Li, Jinjia, Seif, Steve, Brown, David N..*

Subjects/Keywords: commutative algebra; integral domains; monoid domains; factorization; Algebra

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APA (6^{th} Edition):

Gipson, R. H. (2018). Factorization in integral domains. (Doctoral Dissertation). University of Louisville. Retrieved from 10.18297/etd/3056 ; https://ir.library.louisville.edu/etd/3056

Chicago Manual of Style (16^{th} Edition):

Gipson, Ryan H. “Factorization in integral domains.” 2018. Doctoral Dissertation, University of Louisville. Accessed July 10, 2020. 10.18297/etd/3056 ; https://ir.library.louisville.edu/etd/3056.

MLA Handbook (7^{th} Edition):

Gipson, Ryan H. “Factorization in integral domains.” 2018. Web. 10 Jul 2020.

Vancouver:

Gipson RH. Factorization in integral domains. [Internet] [Doctoral dissertation]. University of Louisville; 2018. [cited 2020 Jul 10]. Available from: 10.18297/etd/3056 ; https://ir.library.louisville.edu/etd/3056.

Council of Science Editors:

Gipson RH. Factorization in integral domains. [Doctoral Dissertation]. University of Louisville; 2018. Available from: 10.18297/etd/3056 ; https://ir.library.louisville.edu/etd/3056