Date of Award


Document Type


Degree Name

Master of Science (MS)


School of Mathematical and Statistical Sciences

Committee Chair/Advisor

James Coykendall

Committee Member

Hui Xue

Committee Member

Keri Sather-Wagstaff

Committee Member

Kevin James


We will examine orders R in a number field K. In particular, we will look at how the generalized class number of R relates to the class number of its integral closure R. We will then apply this to the case when K is a quadratic field to produce a more specific relation. After this, we will focus on orders R which are half-factorial domains (HFDs), in which the irreducible factorization of any element αR has fixed length. We will determine two cases in which R is an HFD if and only if its ring of formal power series R[[x]] is an HFD. Finally, we will consider how these strategies may apply (or fail to apply) to more general results.

Author ORCID Identifier




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