ISSN:1308-2140

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Essential G-Supplemented Modules


In this work essential g-supplemented modules are defined and some properties of these modules are investigated. All modules are associative with unity and all modules are unital left modules. Let M be an R-module. If every essential submodule of M has a g-supplement in M, then M is called an essential g-supplemented (or briefly ge-supplemented) module. Clearly we can see that every g-supplemented module is essential g-supplemented. Because of this essential g-supplemented modules are more generalized than g-supplemented modules. Every (generalized) hollow and every local module are essential g-supplemented. Let M be an essential g-supplemented R-module. If every nonzero submodule of M is essential in M, then M is g-supplemented. It is proved that every factor module and every homomorphic image of an essential g-supplemented module are essential g-supplemented. It is also proved that the finite sum of essential g-supplemented modules is essential g-supplemented. Let M be an essential g-supplemented module. Then M/RadgM have no proper essential submodules. Let M be an essential g-supplemented R-module. Then every finitely M-generated R-module is essential g-supplemented. Let R be any ring. Then RR is essential g-supplemented if and only if every finitely generated R-module is essential g-supplemented. Let M be an R-module. If every essential submodule of M is g* equivalent to an essential g-supplement (ge-supplement) submodule in M, then M is essential g-supplemented.


Keywords


Essential Submodules, Small Submodules, Supplemented Modules, G-Supplemented Modules

Yazar: Hasan Hüseyin ÖKTEN - - Celil NEBİYEV
Sayfa Sayısı: 83-89
DOI: http://dx.doi.org/10.7827/TurkishStudies.14874
Tam Metin:
Turkish Studies
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