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On derivations and commutativity of prime rings with involution

  • Shakir Ali EMAIL logo , Nadeem Ahmed Dar and Mustafa Asci
Published/Copyright: April 2, 2015
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Abstract

In [Acta Math. Hungar. 66 (1995), 337–343], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d(xy)=d(yx) for all x,yR, then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d(xx*)=d(x*x) for all xR and S(R)Z(R)(0), then R is commutative. Moreover, some related results have also been discussed.

Funding source: U.G.C.

Award Identifier / Grant number: 39-37/2010(SR)

The authors wish to express their sincere thanks to the referee for his/her valuable suggestions. The first and second authors are grateful for the kind hospitality they received during their stay (August 2013) at Pamukkale University, Turkey.

Received: 2013-11-28
Revised: 2014-6-9
Accepted: 2014-6-11
Published Online: 2015-4-2
Published in Print: 2016-3-1

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