Characteristic modules over a local ring

2024/04/26 by Gheibi, Mohsen, Takahashi, Ryo
#13D05 #13D07 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.17680

Abstract

Let R be a commutative noetherian local ring, and let M be a finitely generated R-module. Inspired by works of Vasconcelos and Briggs on characterization of complete intersection local rings through the homological properties of the conormal module, in this paper, we define the characteristic module T_M and the cocharacteristic module E_M of M, and investigate their properties. Our main results include characterizations of Cohen--Macaulay and Gorenstein local rings.

Related

• Special homological dimensions and Intersection Theorem
• On the existence of certain modules of finite Gorenstein homological dimensions
• On the relative Cohen-Macaulay modules
• Codualizing modules
• Differential modules: a perspective on Bass' question