Abstract
Let R be a ∗-prime ring with involution ∗ and center Z(R). An additive mapping F:R→R is called a semiderivation if there exists a function g:R→R such that (i) F(xy)=F(x)g(y)+xF(y)=F(x)y+g(x)F(y) and (ii) F(g(x))=g(F(x)) hold for all x,y∈R. In the present paper, some well known results concerning derivations of prime rings are extended to semiderivations of ∗-prime rings.
Highlights
Many authors have studied commutativity of prime and semiprime rings admitting derivations, generalized derivations and semiderivations which satisfy appropriate algebraic conditions on suitable subsets of the rings
In the present paper our objective is to generalize above results for semiderivations of a ∗−prime ring
Throughout the paper, R will be a ∗−prime ring and F be a semiderivation of R associated with a surjective function g of R such that ∗F = F ∗
Summary
Many authors have studied commutativity of prime and semiprime rings admitting derivations, generalized derivations and semiderivations which satisfy appropriate algebraic conditions on suitable subsets of the rings. Throughout the paper, R will be a ∗−prime ring and F be a semiderivation of R associated with a surjective function g of R such that ∗F = F ∗ .
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