An -module is extending if every submodule of is essential in a direct summand of . Following Clark, an -module is purely extending if every submodule of is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module is Goldie extending if, for each submodule of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module is purely Goldie extending if, for each , there is a pure submodule P of such that . Many characterizations and properties of purely Goldie extending modules are given. Also, we discuss when a direct sum of purely Goldie extending modules is purely Goldie extending and moreover we give a sufficient condition to make this property of purely Goldie extending modules is valid.
Purely Goldie Extending Modules
extending module
purely extending module
-extending module
purely Goldie extending.
Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Fuzzy Semimaximal Submodules
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if Mâ„(Nis a semisimple R-module ).The main objective of this work is to fuzzify this concept
study the basic properties and we investigate the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple
semisimple) F- submodules and quotient F- modules are introduced and given some properties .
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
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