Amply Essential Supplemented Modules
Celil Nebiyev
Department of Mathematics, Ondokuz Mayıs University, Kurupelit-Atakum, Samsun, Turkey.
Hasan Hüseyin Ökten *
Technical Sciences Vocational School, Amasya University, Amasya, Turkey.
Ayten Pekin
Department of Mathematics, Istanbul University, Vezneciler, Istanbul, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this work, amply essential supplemented modules are defined and some properties of these modules are investigated. We prove that every π−projective and essential supplemented module is amply essential supplemented. We also prove that every factor module and every homomorphic image of an amply essential supplemented module are amply essential supplemented. Let M be a projective and essential supplemented R−module. Then every finitely M−generated R−module is amply essential supplemented.
Keywords: Essential submodules, small submodules, supplemented modules, essential supplemented modules.