MODULES FOR WHICH EVERY SUBMODULE HAS A UNIQUE COCLOSURE

P. F. Smith studied modules in which every submodule has a unique closure and called them UC modules. In this paper we consider modules with the dual property viz., those in which every submodule has a unique coclosure and call such modules UCC modules. Unlike closures, a coclosure of a submodule of...

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Bibliographic Details
Published in:Communications in algebra 2002-05, Vol.30 (5), p.2355-2377
Main Authors: Ganesan, Lalitha, Vanaja, N.
Format: Article
Language:English
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Summary:P. F. Smith studied modules in which every submodule has a unique closure and called them UC modules. In this paper we consider modules with the dual property viz., those in which every submodule has a unique coclosure and call such modules UCC modules. Unlike closures, a coclosure of a submodule of a module may not always exist and even if it exists, it may not be unique. We investigate the conditions under which a module is a UCC module. We prove that UCC modules are closed under factor modules and coclosed submodules. We also investigate their properties and their relation to non-cosingular modules, copolyform modules, and codimension modules. We end this paper with the dual of Smith's result on dimension modules.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120003473