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gorenstein modules

Proceedings of the Edinburgh Mathematical Society (1)

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DUALIZING MODULES AND n-PERFECT RINGS
Edgar E. Enochs, Overtoun M. G. Jenda, J. A. López-Ramos
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 1 / February 2005

Published online by Cambridge University Press:

15 February 2005, pp. 75-90
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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