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Covers and Envelopes via Endoproperties of Modules

Published online by Cambridge University Press:  09 June 2003

Lidia Angeleri-Hügel
Lidia Angeleri-Hügel
Affiliation:
Mathematisches Institut der Universität, Theresienstrasse 39, D-80333 München, Germany Present address: Universitá degli Studi dell'Insubria, Dipartimento di Informatica e Communicazione, Via Mazzini 5, I-21100 Varese, Italy. E-mail: lidia.angeleri@uninsubria.it
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Abstract

Let $R$ be a ring and $M_R$ be an $R$-module. We characterize the existence of ${\rm Add} M$-covers and ${\rm Add} M$-envelopes in terms of finiteness conditions of $M$ over its endomorphism ring. We then present some applications related to the existence of well-behaved direct sum decompositions for direct products of copies of $M$. Our results can be viewed as natural extensions of classical theorems of Bass and Chase on coherent and perfect rings.

Keywords

left/right approximationsendomorphism ringmatrix subgroupperfect ringscoherent rings16D9016G1016S5016D4016P7016E50
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 3 , May 2003 , pp. 649 - 665
Copyright
2003 London Mathematical Society

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