Browsing by Author "Jorgensen, David A."

Now showing items 1-9 of 9

    • Existence of Exact Zero Divisors and Totally Reflexive Modules in Artinian Rings 

      Sharma Poudyal, Basanti; 0000-0001-6149-6116 (2017-05-10)
      In this dissertation, we consider commutative local Artinian rings (A, m, k), which are rings that satisfy the descending chain condition on ideals. First, we investigate the existence of exact zero divisors in Artinian ...

    • On Progenitively Koszul Commutative Rings 

      Stern, Paul Russell (Mathematics, 2008-04-22)
      This paper introduces and identifies classes of progenitively Koszul rings. A progenitively Koszul ring is a commutative ring that admits a Koszul complex A=K(R) that is formal, and such that the homology algebra H(A) ...

    • On The Existence Of Totally Reflexive Modules 

      Beck, Kristen Ann (Mathematics, 2011-07-14)
      In this manuscript, we investigate the existence of non-free totally reflexive modules over two classes of commutative local (Noetherian) rings.First, we demonstrate existence over a class of local rings which are defined ...

    • On The Image Of The Totalling Functor 

      Beck, Kristen Ann (Mathematics, 2007-08-23)
      Let A denote a DG algebra and k a field. The totalling functor, from the category of chain complexes over the graded A-modules to the catagory of DG modules over A, can be extended to one between their derived categories. ...

    • Properties Of The Pinched Tensor Product 

      Alkhezi, Yousuf (Mathematics, 2014-12)
      For complexes of modules we study a new construction, called the pinched tensor product, which was introduced by Lars Winther Christensen and David A. Jorgensen to study Tate homology. We explore properties of the pinched ...

    • Representation Theory Of Totally Reflexive Modules Over non-Gorenstein Rings 

      Rangel, Denise Amanda (Mathematics, 2014-09-17)
      In the late 1960's Auslander and Bridger published Stable Module Theory, in whichthe idea of totally reflexive modules first appeared. These modules have been studiedby many. However, a bulk of the information known about ...

    • Resolutions And Tor Algebra Structures For Trivariate Monomial Ideals 

      Painter, Jared Lafayette (Mathematics, 2012-07-25)
      In this manuscript we explore properties of minimal free resolutions and their relationship to the Tor-algebra structure for trivariate monomial ideals. We begin with an in-depth analysis of minimal free resolutions of ...

    • Support and Rank Varieties of Totally Acyclic Complexes 

      Steele, Nathan Thomas; 0000-0002-6494-2481 (2016-08-12)
      Support and rank varieties of modules over a group algebra of an elementary abelian p-group have been well studied. In particular, Avrunin and Scott showed that in this setting, the rank and support varieties are equivalent. ...

    • The Uniqueness Of Minimal Acyclic Complexes 

      Hughes, Meri Trema (Mathematics, 2009-09-16)
      In this paper, we discuss conditions for uniqueness among minimal acyclic complexes of finitely generated free modules over a commutative local ring which share a common syzygy module. Although such uniqueness occurs over ...