IJPAM: Volume 92, No. 3 (2014)


Majid Mohammed Abed$^1$, Abd Ghafur Ahmad$^2$
$^{1,2}$School of Mathematical Sciences
Faculty of Science and Technology
Universiti Kebangsaan Malaysia
43600 UKM, Selangor Darul Ehsan, MALAYSIA

Abstract. In this paper we give explicit necessary and sufficient conditions for weak-$\bigoplus$-supplemented module. If $M$ is lifting module then it is weak-$\bigoplus$-supplemented module. Moreover if we have an $R$-module $M$ such that is generalized lifting module then $M$ is weak-$\bigoplus$-supplemented module. We prove that if $M$ is supplemented and projective then $M$ is weak-$\bigoplus$-supplemented.

Received: July 6, 2013

AMS Subject Classification: 54C05, 54C08, 54C10

Key Words and Phrases: $\bigoplus$-supplemented module, amply supplemented module, weak lifting module, semisimple module, generalization lifting module

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DOI: 10.12732/ijpam.v92i3.3 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 3
Pages: 351 - 358

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).