TY  - JOUR
TI  - COFINITELY ESSENTIAL SUPPLEMENTED MODULES
AB  - In this work, cofinitely essential supplemented modules aredefined and some properties of these modules are investigated. All ringswill be associative with identity and all modules will be unital leftmodules in this work. Let M be an R-module. If every cofinite essentialsubmodule of M has a supplement in M, then M is called a cofinitelyessential supplemented (or briefly cofinitely e-supplemented) module.Clearly we can see that every cofinitely supplemented module iscofinitely essential supplemented. Because of this cofinitely essentialsupplemented modules are more generalized than cofinitelysupplemented modules. Every essential supplemented module iscofinitely essential supplemented and every finitely generated cofinitelyessential supplemented module is essential supplemented. Let M be acofinitely essential supplemented R-module. If every nonzero submoduleof M is essential in M, then M is cofinitely supplemented. It is provedthat every factor module and every homomorphic image of a cofinitelyessential supplemented module are cofinitely essential supplemented. Itis also proved that any sum of cofinitely essential supplementedmodules is cofinitely essential supplemented. Let M be a cofinitelyessential supplemented module. Then M/RadM have no proper cofiniteessential submodules. Let M be a cofinitely essential supplemented R-module. Then every M-generated R-module is cofinitely essentialsupplemented. Let R be any ring. Then R R is essential supplemented ifand only if every R-module is cofinitely essential supplemented.
AU  - KOŞAR, Berna
AU  - Nebiyev, Celil
DO  - 10.7827/TurkishStudies.14492
PY  - 2018
JO  - Turkish Studies (Elektronik)
VL  - 13
IS  - 29
SN  - 1308-2140
SP  - 83
EP  - 88
DB  - TRDizin
UR  - http://search/yayin/detay/303501
ER  -