• A class of Gorenstein Artin algebras of embedding dimension four 

    El Khoury, Sabine, 1978- (University of Missouri--Columbia, 2007)
    Let R be a polynomial ring in n variables and I be a homogeneous ideal in R. Such an ideal I is called Gorenstein if the quotient R/I has a free resolution over R which is both self dual. In 2005 Iarrobino and Srinivasan ...
  • Minimal homogeneous resolutions, almost complete intersections and Gorenstein Artin algebras 

    Seo, Sumi (University of Missouri-Columbia, 2011)
    This work is devoted to the study of the structures of the graded resolutions of codimension three almost complete intersections and the unimodality and SI-sequence of Hilbert functions of Gorenstein Artin algebras in ...
  • Minimal resolutions for a class of Gorenstein determinantal ideals 

    Hulsizer, Heidi, 1982- (University of Missouri--Columbia, 2010)
    Let X = {x[subscript ij]} [subscript mxn] be a matrix with entries in a noetherian commutative ring R. I[subscript t](X) denotes the determinantal ideal generated by the t x t minors of X. The ideals are called generic if ...
  • On the periodicity of the first Betti number of the semigroup ring under translations 

    Marzullo, Adriano, 1972- (University of Missouri--Columbia, 2010)
    Any curve C in any dimension can be described by a parameterization. In particular in the plane, that is dimension 2, the coordinates x and y are both given as a function of a third variable t, called parameter: x=x(t), ...
  • On unimodality of Hilbert functions of Artinian level algebras of codimension 3 and type 2 and 3 

    D'Orazio, Valeria, 1979- ([University of Missouri--Columbia], 2014)
    We prove the unimodality of the Hilbert Function for some classes of codimension three graded algebras of Cohen-Macaulay types 2 and 3. The method of proof uses the explicit structure theorems similar to the structure ...
  • Results on the Collatz Conjecture 

    Hardwick, Samuel ([University of Missouri--Columbia], 2014)
    Given a starting value, we can create a sequence using the rule that if the previous number, x, is even, then the next number is [x/2], and if the previous number, x, is odd, then the next number is [(3x+1)/2]. The collatz ...