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ON A DUALITY THEOREM OF WAKAMATSU

Part of: Modules, bimodules and ideals Homological methods

Published online by Cambridge University Press:  01 October 2008

ZHAOYONG HUANG
ZHAOYONG HUANG*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: [email protected])
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Abstract

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Let R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S=End(RU) satisfying the condition that each finitely presented left R-module X with ExtRi(X,U)=0 for any i≥1 is U-torsionless. If M is a finitely presented left R-module such that ExtRi(M,U)=0 for any i≥0 with (where n is a nonnegative integer), then and ExtSi(ExtRn(M,U),U)=0 for any i≥0 with . A duality is thus induced between the category of finitely presented holonomic left R-modules and the category of finitely presented holonomic right S-modules.

Keywords

generalized tilting modulesU-torsionless propertyFP-injective dimension

MSC classification

Secondary: 16E30: Homological functors on modules (Tor, Ext, etc.) 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 343 - 350
Copyright
Copyright © 2008 Australian Mathematical Society

References

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