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Modules whose closed submodules are finitely generated

Published online by Cambridge University Press:  20 January 2009

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

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A module M is called a CC-module if every closed submodule of M is cyclic. It is shown that a cyclic module M is a direct sum of indecomposable submodules if all quotients of cyclic submodules of M are CC-modules. This theorem generalizes a recent result of B. L. Osofsky and P. F. Smith on cyclic completely CS-modules. Some further applications are given for cyclic modules which are decomposed into projectives and injectives.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 1 , February 1991 , pp. 161 - 166
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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