IJPAM: Volume 113, No. 5 (2017)

Title

COMMUTATIVITY OF $\sigma $-PRIME
$\Gamma $-RINGS WITH SEMIDERIVATIONS

Authors

K.K. Dey$^2$, A.C. Paul$^2$, I.S. Rakhimov$^3$
$^{1,2}$Department of Mathematics
Rajshahi University
Rajshahi, 6205, BANGLADESH
$^{3}$Department of Mathematics
Institute for Mathematical Research
Universiti Putra Malaysia
MALAYSIA

Abstract

Let $M$ be a 2-torsion free $\sigma $-prime $\Gamma $-ring satisfying the condition $a\alpha b\beta c=a\beta b\alpha c$ for all $a,b,c\in M$ and $\alpha $, $\beta \in \Gamma $, $I$ a $\sigma $-prime ideal of $M$ and $d$ a semiderivation associated with a function $g$ which is surjective on $I$. In the paper we show some conditions on $d$, such that $d = 0$ or $M$ is commutative.

History

Received: July 5, 2016
Revised: March 20, 2017
Published: April 1, 2017

AMS Classification, Key Words

AMS Subject Classification: 6W10, 16W25, 16U80
Key Words and Phrases: $\sigma $-prime $\Gamma $-ring, $\sigma $-ideal, semiderivation, involution

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v113i5.2 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: 113
Issue: 5
Pages: 541 - 552


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