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Applications of Groups of Divisibility and a Generalization of Krull Dimension
(North Dakota State University, 2011)
Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a ...
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 ...
The Game of Nim on Graphs
(North Dakota State University, 2011)
The ordinary game of Nim has a long history and is well-known in the area of combinatorial game theory. The solution to the ordinary game of Nim has been known for many years and lends itself to numerous other solutions ...