IJPAM: Volume 115, No. 1 (2017)

Title

STRONGLY T-SEMISIMPLE MODULES AND
STRONGLY T-SEMISIMPLE RINGS

Authors

Inaam Mohammed Ali Hadi$^1$, Farhan Dakhil Shyaa$^2$
$^1$Department of Mathematics
University of Baghdad
Baghdad, IRAQ
and
College of Education for Pure Sciences (Ibn-Al-Haitham)
University of Baghdad, Baghdad, IRAQ
$^2$Department of Mathematics University of Al-Qadisiyah
College of Education, Al-Qadisiya, IRAQ

Abstract

In this paper, we introduce the notions of strongly t-semisimple modules and strongly t-semisimple rings as a generalization of semisimple modules, rings respectively. We investigate many characterizations and properties of each of these concepts. An R-module is called strongly t-semisimple if for each submodule N of M there exists a fully invariant direct summand K such that K t-essential in N. Also, the direct sum of strongly t-semisimple modules and homomorvarphic image of strongly t-semisimple is strongly t-semisimple.

A ring R is called right strongly t-semisimple if $R_{R}$ is strongly t-semisimple. Various characterizations of right strongly t-semisimple rings are given.

History

Received: December 25, 2016
Revised: March 22, 2017
Published: June 29, 2017

AMS Classification, Key Words

AMS Subject Classification: 16D10, 16D70, 16D90, 16P70
Key Words and Phrases: strongly t-semisimple, t-semismiple modules

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How to Cite?

DOI: 10.12732/ijpam.v115i1.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 1
Pages: 27 - 41


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