TL;DR
This paper introduces quasidualizing modules, exploring their properties and relationships with semidualizing modules through Matlis duality, and analyzing their connections with Auslander and Bass classes.
Contribution
It defines quasidualizing modules, establishes their connection to semidualizing modules via Matlis duality, and investigates their role in derived T-reflexive modules.
Findings
Quasidualizing modules are characterized by specific homothety and Ext vanishing conditions.
They are linked to semidualizing modules through Matlis duality.
The study reveals relationships between Auslander and Bass classes via quasidualizing modules.
Abstract
We introduce and study "quasidualizing" modules. An artinian R-module T is quasidualizing if the homothety map \hat R\rightarrow Hom(T,T) is an isomorphism and Ext_R^i(T,T)=0 for each integer i>0. Quasidualizing modules are associated to semidualizing modules via Matlis duality. We investigate the associations via Matlis duality between subclasses of the Auslander class and Bass class and subclasses of derived T-reflexive modules.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras