Date of Award
2015
Publisher
North Dakota State University
Document Type
Thesis
Degree Awarded
Master of Science (MS)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
Duncan, Benton
Description
The goal of this thesis is to provide an new generalization of Cohen-Kaplansky domains, stemming from questions related to valuation domains. Recall that a Cohen-Kaplansky domain is an atomic integral domain that contains only a nite number of irreducible elements (up to units). In the new generalization presented in this thesis, we remove the atomic condition required in the de nition of a Cohen-Kaplansky domain and add in the extra condition that our integral domain has nitely many irreducible elements, say 1; 2; ; n, such that for every nonzero nonunit y in the domain there exists an irreducible element, say i with 1 i n, such that i j y.
Recommended Citation
Kennedy, Diana Michelle, "A New Generalization of Cohen-Kaplansky Domains" (2015). Mathematics. 26.
https://digitalcommons.ndsu.edu/mathematics/26
Rights
NDSU Policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/27876