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WEAK INJECTIVE AND WEAK FLAT COMPLEXES

Published online by Cambridge University Press:  21 July 2015

ZENGHUI GAO
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, P.R. China College of Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan Province, P.R. China e-mail: [email protected]
ZHAOYONG HUANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, P.R. China e-mail: [email protected]
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Abstract

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Let R be an arbitrary ring. We introduce and study a generalization of injective and flat complexes of modules, called weak injective and weak flat complexes of modules respectively. We show that a complex C is weak injective (resp. weak flat) if and only if C is exact and all cycles of C are weak injective (resp. weak flat) as R-modules. In addition, we discuss the weak injective and weak flat dimensions of complexes of modules. Finally, we show that the category of weak injective (resp. weak flat) complexes is closed under pure subcomplexes, pure epimorphic images and direct limits. As a result, we then determine the existence of weak injective (resp. weak flat) covers and preenvelopes of complexes.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

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