Quasidualizing modules

Abstract

We introduce and study ``quasidualizing" modules. An artinian $R$-module $T$ is \emph{quasidualizing} if the homothety map $\comp R\rightarrow\hom TT$ is an isomorphism and $\Ext{i}{T}{T}=0$ for each integer $i>0$. Quasidualizing modules are associated to semidualizing modules via Matlis duality. %We study the properties of %quasidualizing modules. An $R$-module $L$ is \emph{derived $T$-reflexive} if %the map $L\rightarrow\hom{\hom LT}{T}$ is an isomorphism %and $\Ext{i}{L}{T}=0=\Ext{i}{\hom LT}{T}$ for each integer $i>0$. We investigate the associations via Matlis duality between subclasses of the Auslander class and Bass class and subclasses of derived $T$-reflexive modules.