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Modules whose closed submodules are finitely generated
Published online by Cambridge University Press: 20 January 2009
Abstract
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
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