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A note on existence of envelopes and covers

Published online by Cambridge University Press:  17 April 2009

Jianlong Chen  and
Nanqing Ding
Jianlong Chen
Affiliation:
Department of Mathematics and Mechanics, Southeast University, Nanjing 210096, People's Republic of China
Nanqing Ding
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China
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Abstract

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We prove the following results for a ring R. (a) If C is a class of right R-modules closed under direct summands and isomorphisms, then every right R-module has an epic C-envelope if and only if C is closed under direct products and submodules. (b) If R is left T-coherent and pure injective as a right R-module, then every T-finitely presented right R-module has a T-flat envelope, (c) Let R be a left T-coherent ring and injective right R-modules be T-flat. If every finitely presented left R-module has a flat envelope, then every T-finitely presented right R-module has a projective cover.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 383 - 390
Copyright
Copyright © Australian Mathematical Society 1996

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