$C$-CANONICAL MODULES

Year 2021, Volume: 30 Issue: 30, 243 - 259, 17.07.2021

Mohammad Bagherı Abdol-javad Taherızadeh

https://doi.org/10.24330/ieja.969917

Cited By: 2

https://izlik.org/JA76JZ78JK

Abstract

Let $C$ be a semidualizing module over a commutative Noetherian local ring $R$. In this paper we introduce a new class of modules, namely $C$-canonical modules which are a generalization of canonical modules. It is shown that if the canonical module exists then the $C$-canonical module exists and the converse holds under special conditions. Also, a new characterization of Gorenstein local rings is given via $C$-canonical modules.

Keywords

Semidualizing modules , dualizing modules , local cohomology , Auslander class , Bass class

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