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On μ -singular and μ -extending modules

Yahya Talebi, Ali Reza Moniri Hamzekolaee (2012)

Archivum Mathematicum

Let M be a module and μ be a class of modules in Mod - R which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a μ -essential submodule provided it has a non-zero intersection with any non-zero submodule in μ . We define and investigate μ -singular modules. We also introduce μ -extending and weakly μ -extending modules and mainly study weakly μ -extending modules. We give some characterizations of μ -co-H-rings by weakly μ -extending modules. Let R ...

Ordinary selfdistributive rings

Sobhy Ghoneim, Marian Kechlibar, Tomáš Kepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Left selfdistributive rings (i.e., x y z = x y x z ) which are semidirect sums of boolean rings and rings nilpotent of index at most 3 are studied.

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