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coherent rings

Proceedings of the London Mathematical Society (1)

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Covers and Envelopes via Endoproperties of Modules
Lidia Angeleri-Hügel
Journal:

Proceedings of the London Mathematical Society / Volume 86 / Issue 3 / May 2003

Published online by Cambridge University Press:

09 June 2003, pp. 649-665

Print publication:

May 2003
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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.