Systems of parameters and the Cohen-Macaulay property

Authors

Katharine Shultis, University of Nebraska-LincolnFollow

Date of this Version

8-2015

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Srikanth B. Iyengar and Roger Wiegand. Lincoln, Nebraska: August, 2015

Copyright (c) 2015 Katharine Shultis

Abstract

Let R be a commutative, Noetherian, local ring and M a finitely generated R-module. Consider the module of homomorphisms Hom_R(R/a,M/bM) where b [subset of] a are parameter ideals of M. When M = R and R is Cohen-Macaulay, Rees showed that this module of homomorphisms is isomorphic to R/a, and in particular, a free module over R/a of rank one. In this work, we study the structure of such modules of homomorphisms for a not necessarily Cohen-Macaulay R-module M.