IJPAM: Volume 109, No. 4 (2016)

SOME RESULTS ON SEMIGROUP IDEALS
IN PRIME RING WITH DERIVATIONS

Ayşe Ayran$^1$, Neşet Aydın$^2$
$^{1,2}$Department of Mathematics
Çanakkale Onsekiz Mart University
Çanakkale, TURKEY

Abstract. Let $R$ be a prime ring, $I$ be a nonzero semigroup ideal of $R$, $d,g,h$ be derivations of $R$ and $a,b\in R$. It is proved that if $d(x)=ag(x)+h(x)b$ for all $x\in I$ and $a,b$ are not in $Z(R)$ then there exists for some $\lambda\in C$ such that $h(x)=\lambda\left[ a,x\right] $, $g(x)=\lambda \left[ b,x\right] $ and $d(x)=\lambda\left[ ab,x\right] $ for all $x\in I.$

Received: May 5, 2016

Revised: August 12, 2016

Published: October 9, 2016

AMS Subject Classification: 16N60, 16U80

Key Words and Phrases: prime ring, semigroup ideal, martindale quotient ring, extended centroid
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Bibliography

1
M. Bresar, Centralizing mapping and derivations in prime rings, Journal of Algebra, 156 (1993), 385-394.

2
I.N. Herstein, Ring With Involution, Univ. of Chicago Press., Chicago (1976).

3
I.N. Herstein, A note on derivations, II, Canad. Math. Bull., 22, No. 4 (1979), 509-511.

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DOI: 10.12732/ijpam.v109i4.14 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: 2016
Volume: 109
Issue: 4
Pages: 911 - 918


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