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On indecomposable decompositions of CS-modules

Published online by Cambridge University Press:  09 April 2009

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

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

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