Displaying similar documents to “On Jordan ideals and derivations in rings with involution”

On left ( θ , ϕ ) -derivations of prime rings

Mohammad Ashraf (2005)

Archivum Mathematicum

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Let R be a 2 -torsion free prime ring. Suppose that θ , φ are automorphisms of R . In the present paper it is established that if R admits a nonzero Jordan left ( θ , θ ) -derivation, then R is commutative. Further, as an application of this resul it is shown that every Jordan left ( θ , θ ) -derivation on R is a left ( θ , θ ) -derivation on R . Finally, in case of an arbitrary prime ring it is proved that if R admits a left ( θ , φ ) -derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal...

On Lie ideals and Jordan left derivations of prime rings

Mohammad Ashraf, Nadeem-ur-Rehman (2000)

Archivum Mathematicum

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Let R be a 2-torsion free prime ring and let U be a Lie ideal of R such that u 2 ∈ U for all u ∈ U . In the present paper it is shown that if d is an additive mappings of R into itself satisfying d ( u 2 ) = 2 u d ( u ) for all u ∈ U , then d ( u v ) = u d ( v ) + v d ( u ) for all u , v ∈ U .