Rad-⊕-Supplemented Modules and Cofinitely Rad-⊕-Supplemented Modules-Reference-Cited by-同舟云学术

Rad-⊕-Supplemented Modules and Cofinitely Rad-⊕-Supplemented Modules

Published:2012-10-15 Issue:04 Volume:19 Page:637-648
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Ecevit Şule¹,Koşan Muhammet T.¹,Tribak Rachid²

Affiliation:

1. Department of Mathematics, Gebze Institute of Technology, Çayirova Campus 41400 Gebze - Kocaeli, Turkey

2. Département de Mathématiques, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, B.P. 21.21. Tétouan, Morocco

Abstract

A module M is called (cofinitely) Rad-⊕-supplemented if every (cofinite) submodule of M has a Rad-supplement that is a direct summand of M. We prove that if M is a coatomic cofinitely Rad-⊕-supplemented module, then M is an irredundant sum of local direct summands. We show that the classes of cofinitely Rad-⊕-supplemented modules and Rad-⊕-supplemented modules are closed under finite direct sums. We also show that every direct summand of a weak duo (cofinitely) Rad-⊕-supplemented module is (cofinitely) Rad-⊕-supplemented.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386712000508

Reference12 articles.

1. ON A RECENT GENERALIZATION OF SEMIPERFECT RINGS

2. Frontiers in Mathematics;Clark J.,2006

3. A. Idelhadj and R. Tribak, Algebra and Number Theory (Fez), Lecture Notes in Pure and Appl. Math. 208 (Marcel Dekker, New York, 2000) pp. 149–155.

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Strongly ⊕−g−radical supplemented modules;Miskolc Mathematical Notes;2023

2. Rad−⊕−supplemented lattices;Miskolc Mathematical Notes;2023

3. On Semiregular Endomorphism Rings and the Dual of Yamagata’s Theorem;Acta Mathematica Vietnamica;2021-06-30

4. I-Rad-⊕-supplemented modules;Acta Universitatis Sapientiae, Mathematica;2019-08-01

5. G– $$\delta$$ δ –M Modules and Torsion Theory Cogenerated by Such Modules;Iranian Journal of Science and Technology, Transactions A: Science;2017-03-27