Turkish Studies - Information Technologies and Applied Sciences, vol.14, no.1, pp.83-89, 2019 (Peer-Reviewed Journal) identifier


In this work essential g-supplemented modules are defined andsome properties of these modules are investigated. All modules areassociative with unity and all modules are unital left modules. Let M bean R-module. If every essential submodule of M has a g-supplement inM, then M is called an essential g-supplemented (or briefly gesupplemented) module. Clearly we can see that every g-supplementedmodule is essential g-supplemented. Because of this essential gsupplemented modules are more generalized than g-supplementedmodules. Every (generalized) hollow and every local module are essentialg-supplemented. Let M be an essential g-supplemented R-module. If everynonzero submodule of M is essential in M, then M is g-supplemented. Itis proved that every factor module and every homomorphic image of anessential g-supplemented module are essential g-supplemented. It is alsoproved that the finite sum of essential g-supplemented modules isessential g-supplemented. Let M be an essential g-supplemented module.Then M/RadgM have no proper essential submodules. Let M be anessential g-supplemented R-module. Then every finitely M-generated Rmodule is essential g-supplemented. Let R be any ring. Then RR isessential g-supplemented if and only if every finitely generated R-moduleis essential g-supplemented. Let M be an R-module. If every essentialsubmodule of M is g* equivalent to an essential g-supplement (gesupplement) submodule in M, then M is essential g-supplemented.