• Commutative Rings whose Prime Spectra have certain Arithmetical Closure Properties 

        Author(s):Karn, Jacob Daniel
        Date Submitted:2018-08
        In this thesis, we consider two questions. First, let R be a commutative ring with identity. Suppose the collection of prime ideals of R is closed under ideal multiplication. What does this condition imply about the ideal ...
      • Set-Theoretic Approach to Obtaining Infinity, A 

        Author(s):Jones, Matthew Michael
        Date Submitted:2016-12
        Many set-theoretic axioms have been formulated over the years which imply (along with the other axioms for set theory) the existence of what one would intuitively regard as an infinite set. In this thesis, we identify a ...
      • Traceless Matrices that are not Commutators 

        Author(s):Saito, Ikuko
        Date Submitted:2016-05
        By a classical result, for any field F and a positive integer n, a matrix in Mn(F) is a commutator if only and if it has trace zero. This is no longer true if F is replaced with an arbitrary ring R. But the only known ...
      • Lower Finite Modules Over Commutative Rings With Identity 

        Author(s):Harmon, Luke Everett
        Date Submitted:2020-05
        A bounded partially ordered set (P, 0, 1, ≤) is lower finite providedP is infinite and for each x 6= 1 in P, there are but finitely many elements y in Psuch that y < x. We will call a module M lower finite if the set of ...