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When are multiplicative semi-derivations additive?

  • Mohammad Aslam Siddeeque EMAIL logo und Nazim Khan
Veröffentlicht/Copyright: 12. November 2021
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Abstract

Let R be an associative ring. A multiplicative semi-derivation d is a map on R satisfying

d ( x y ) = d ( x ) g ( y ) + x d ( y ) = d ( x ) y + g ( x ) d ( y ) and d ( g ( x ) ) = g ( d ( x ) )

for all x , y R , where g is any map on R. In this paper, we have obtained some conditions on R, which make d additive. Finally, we have also shown that every multiplicative semi-derivation on M n ( ) , the algebra of all n × n matrices over the field of complex numbers, is an additive derivation.

MSC 2010: 16W20; 16W25

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Received: 2020-07-12
Revised: 2021-03-29
Accepted: 2021-04-12
Published Online: 2021-11-12
Published in Print: 2022-02-01

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