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On indecomposable decompositions of CS-modules

Part of: Local rings and generalizations Modules, bimodules and ideals

Published online by Cambridge University Press:  09 April 2009

Nguyen V. Dung
Nguyen V. Dung
Affiliation:
Institute of MathematicsP.O. Box 631 Bo Ho Hanoi, Vietnam
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Abstract

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It is shown that, over any ring R, the direct sum M = ⊕i∈IMi of uniform right R-modules Mi with local endomorphism rings is a CS-module if and only if every uniform submodule of M is essential in a direct summand of M and there does not exist an infinite sequence of non-isomorphic monomorphisms , with distinct in ∈ I. As a consequence, any CS-module which is a direct sum of submodules with local endomorphism rings has the exchange property.

MSC classification

Secondary: 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation 16D50: Injective modules, self-injective rings 16L60: Quasi-Frobenius rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 30 - 41
Copyright
Copyright © Australian Mathematical Society 1996

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