Journal
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
Volume 48, Issue -, Pages 75-90Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0013091503001056
Keywords
n-perfect ring; dualizing module; Gorenstein modules
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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.
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