When are multiplicative semi-derivations additive?
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 ) ) {d(xy)=d(x)g(y)+xd(y)=d(x)y+g(x)d(y)\quad\text{and}\quad d(g(x))=g(d(x))} for all x , y ∈ R {x,y\in 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 ( ℂ ) {M_{n}(\mathbb{C})} , the algebra of all n × n {n\times n} matrices over the field ℂ {\mathbb{C}} of complex numbers, is an additive derivation.
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2009 ◽
Vol 52
(2)
◽
pp. 267-272
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2010 ◽
Vol 10
(02)
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pp. 291-313
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