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STRONGLY GENERALIZED (WEAKLY) δ-SUPPLEMENTED MODULES


FIGEN ERYILMAZ
Ondokuz Mayis University, Department of Mathematics Education, Kurupelit, Atakum, Samsun, TURKEY
e-mail: fyuzbasi@omu.edu.tr

Issue:

SSRSMI, Number 1, Volume XXVII

Section:

Volume 27, Number 1

Abstract:

In this paper, we introduce strongly generalized (weakly) δ-supplemented modules. We call a module strongly generalized (weakly) δ-supplemented (briefly δ-SGS (δ-SWGS)) if every submodule containing the δ-radical has a (weak) δ-supplement. The first part of this paper investigates various properties of δ-SGS modules. We prove that δ-SGS modules are closed under factor modules and finite sums. Using these modules, we show that a ring R is δ-semiperfect if and only if every left R-module is a δ-SGS module. The second part of this paper establishes some properties of δ-SWGS modules.

Keywords:

δ-small submodule, ( weak) δ-supplement, generalized (weak) δ-supplement, δ-semiperfect ring.

Code [ID]:

SSRSMI201701V27S01A0002 [0004603]

Note:

Full paper:

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