Document Type
Presentation Abstract
Presentation Date
3-13-2017
Abstract
Let R be a commutative, Noetherian, local ring and M a finitely generated R-module. Consider the module of homomorphisms \operatorname{Hom}_R(R/\mathfrak{a},M/\mathfrak{b} M) where \mathfrak{b}\subseteq\mathfrak{a} are parameter ideals of M. When M=R and R is Cohen-Macaulay, Rees showed that this module of homomorphisms is always isomorphic to R/\mathfrak{a}. Recently, K. Bahmanpour and R. Naghipour showed that if \operatorname{Hom}_R(R/\mathfrak{a},R/\mathfrak{b}) is isomorphic to R/\mathfrak{a} for every pair of parameter ideals \mathfrak{b}\subseteq\mathfrak{a} then R is Cohen-Macaulay. In this talk, we will define the terms above and discuss the structure of \operatorname{Hom}_R(R/\mathfrak{a},M/\mathfrak{b}M) for general R.
Download the attached PDF to see the abstract with proper math formatting.
Recommended Citation
Shultis, Katharine, "Systems of parameters and the Cohen-Macaulay property" (2017). Colloquia of the Department of Mathematical Sciences. 523.
https://scholarworks.umt.edu/mathcolloquia/523
Additional Details
Monday, March 13, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109