Amply Cofinitely Essential Supplemented Modules
Berna Koşar
Faculty of Health Sciences, Űsküdar University, Turkey.
Celil Nebiyev *
Department of Mathematics, Ondokuz Mayıs University, Kurupelit-Atakum/Samsun/T¨ürkIye, Turkey.
*Author to whom correspondence should be addressed.
Abstract
Let M be an R−module. If every cofinite essential submodule of M has ample supplements in M then M is called an amply cofinitely essential supplemented module. In this work some properties of these modules are investigated. Let M be a projective and cofinitely essential supplemented R−module. Then every M−generated R−module is amply cofinitely essential supplemented.
Keywords: Essential submodules, cofinite submodules, small submodules, supplemented modules.