Mohamad Nagy Daif

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Let R be a 2−torsion free semiprime ring such that R has a commutator which is not a zero divisor and G: R−→R be an additive mapping such that G(xyx) = G(x)yx + xD(yx) holds for all x, y ∈ R for some derivation D. Then G is a generalized derivation. Mathematics Subject Classification: 16W10, 16E99
The purpose of this note is to prove the following result. Suppose R is a 2-torsion free semiprime *-ring such that R has a commutator which is not a zero divisor and let G : R → R be an additive mapping such that G(xx∗) = G(x)x∗ + xD(x∗) is fulfilled for all x ∈ R, for some derivation D of R. In this case G is a generalized derivation on R. Mathematics(More)
The purpose of this note is to prove the following result. Let R be a semiprime ring of characteristic not 2 and G: R−→R be an additive mapping such that G(x2) = G(x)x + xD(x) holds for all x ∈ R and some derivations D of R. Then G is a Jordan generalized derivation. Mathematics Subject Classification: 16W10, 16W25, 16W20
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