Browsing by Subject "Commutative rings."

Now showing items 1-3 of 3

    • Applications of Groups of Divisibility and a Generalization of Krull Dimension 

      Trentham, William Travis (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 

      Trentham, Stacy Michelle (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 ...

    • Colorings of Zero-Divisor Graphs of Commutative Rings 

      Ramos, Rebecca Elizabeth (North Dakota State University, 2015)
      We will focus on Beck’s conjecture that the chromatic number of a zero-divisor graph of a ring R is equal to the clique number of the ring R. We begin by calculating the chromatic number of the zero-divisor graphs for some ...