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FINITELY GENERATED δ-SUPPLEMENTED MODULES ARE AMPLY δ-SUPPLEMENTED

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  07 February 2012

RACHID TRIBAK
RACHID TRIBAK*
Affiliation:
Centre Pédagogique Régional (CPR) – Tanger, Avenue My Abdelaziz, Souani, BP : 3117, Tangier, Morocco (email: tribak12@yahoo.com)
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Abstract

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Let R be a commutative ring. It is shown that if an R-module M is a sum of δ-local submodules and a semisimple projective submodule, then every finitely generated submodule of M is δ-supplemented. From this result, we conclude that finitely generated δ-supplemented modules over commutative rings are amply δ-supplemented.

Keywords

δ-small submoduleδ-local modulem-δ-local moduleδ-supplemented moduleamply δ-supplemented module

MSC classification

Secondary: 16D10: General module theory 16D99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 430 - 438
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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