Algebra Seminar: Strong test ideals of Stanley-Reisner rings
Strong test ideals of Stanley-Reisner rings
Irina Ilioaea, Department of Mathematics and Statistics, Georgia State University
The main purpose of this talk is to show how we can determine strong test ideals of Stanley-Reisner rings using an algorithm of Katzman and Schwede. The main result of the talk states that the number of generators of the test ideal associated to pairs of Stanley-Reisner rings and linear maps is actually the number of facets of the simplicial complex associated to the Stanley-Reisner ideal. An important consequence of this result is that every element belonging to the tight closure of a square-free monomial ideal I satisfies an integral dependence equation of degree equal to the number of facets of the simplicial complex associated to the ideal I over I.