Date of Award
2014
Publisher
North Dakota State University
Document Type
Dissertation
Degree Awarded
Doctor of Philosophy (PhD)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
Coykendall, Jim
Description
This dissertation investigates the following question: If R is a half-factorial domain (HFD) and x is an indeterminate, under what conditions is the polynomial ring R[x] an HFD? The question has been answered in a few special cases. A classical result of Gauss states that if R is a UFD, then R[x] is a UFD. Also, Zaks showed that if R is a Krull domain with class group Cl(R), then R[x] is an HFD if and only if jCl(R)j 6 2. In the proof of his result, Zaks did not use Gauss's methods. We give a new proof that does. We also study the question in domains other than Krull domains.
Recommended Citation
Batell, Mark Thomas, "The Half-Factorial Property in Polynomial Rings" (2014). Mathematics. 33.
https://digitalcommons.ndsu.edu/mathematics/33
Rights
NDSU Policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/27311