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Atomicity in Rings with Zero Divisors
(North Dakota State University, 2011)
In this dissertation, we examine atomicity in rings with zero divisions. We begin by examining the relationship between a ring’s level of atomicity and the highest level of irreducibility shared by the ring’s irreducible ...
Ramification and Infinite Extensions of Dedekind Domains
(North Dakota State University, 2010)
This dissertation presents methods for determining the behavior of prime ideals
m an integral extension of a Dedekind domain. One tool used to determine this
behavior is an algorithm that computes which prime ideals ...