Applications and homological properties of local rings with decomposable maximal ideals

Authors

• Saeed Nasseh, Georgia Southern UniversityFollow
• Sean Sather-Wagstaff, Clemson UniversityFollow
• Ryo Takahashi, Nagoya UniversityFollow
• Keller VandeBogert, University of KentuckyFollow

Abstract

We construct a local Cohen–Macaulay ring R with a prime ideal p∈Spec(R) such that R satisfies the uniform Auslander condition (UAC), but the localization R_p does not satisfy Auslander's condition (AC). Given any positive integer n, we also construct a local Cohen–Macaulay ring R with a prime ideal p∈Spec(R) such that R has exactly two non-isomorphic semidualizing modules, but the localization R_p has 2ⁿ non-isomorphic semidualizing modules. Each of these examples is constructed as a fiber product of two local rings over their common residue field. Additionally, we characterize the non-trivial Cohen–Macaulay fiber products of finite Cohen–Macaulay type.

Document Type

Article

Publication Date

3-1-2019

Notes/Citation Information

Publisher Copyright: © 2018 Elsevier B.V.

Digital Object Identifier (DOI)

10.1016/j.jpaa.2018.06.006

Archival?

Archival

Repository Citation

Nasseh, Saeed; Sather-Wagstaff, Sean; Takahashi, Ryo; and VandeBogert, Keller, "Applications and homological properties of local rings with decomposable maximal ideals" (2019). Mathematics Faculty Publications. 81.
https://uknowledge.uky.edu/math_facpub/81