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DUALIZING MODULES AND n-PERFECT RINGS

Published online by Cambridge University Press:  15 February 2005

Edgar E. Enochs ,
Overtoun M. G. Jenda  and
J. A. López-Ramos
Edgar E. Enochs
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA (enochs@ms.uky.edu)
Overtoun M. G. Jenda
Affiliation:
Department of Mathematics, Auburn University, AL 36848-5310, USA (jendaov@mail.auburn.edu)
J. A. López-Ramos
Affiliation:
Departamento de Algebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain (jlopez@ual.es)
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Abstract

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In this article we extend the results about Gorenstein modules and Foxby duality to a non-commutative setting. This is done in §3 of the paper, where we characterize the Auslander and Bass classes which arise whenever we have a dualizing module associated with a pair of rings. In this situation it is known that flat modules have finite projective dimension. Since this property of a ring is of interest in its own right, we devote §2 of the paper to a consideration of such rings. Finally, in the paper’s final section, we consider a natural generalization of the notions of Gorenstein modules which arises when we are in the situation of §3, i.e. when we have a dualizing module.

AMS 2000 Mathematics subject classification: Primary 16D20

Keywords

n-perfect ringdualizing moduleGorenstein modules
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 75 - 90
Copyright
Copyright © Edinburgh Mathematical Society 2005