Displaying similar documents to “On centralizers of semiprime rings”

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 Jordan ideals and derivations in rings with involution

Lahcen Oukhtite (2010)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a 2 -torsion free * -prime ring, d a derivation which commutes with * and J a * -Jordan ideal and a subring of R . In this paper, it is shown that if either d acts as a homomorphism or as an anti-homomorphism on J , then d = 0 or J ⊆ Z ( R ) . Furthermore, an example is given to demonstrate that the * -primeness hypothesis is not superfluous.

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 .

Free actions on semiprime rings

Muhammad Anwar Chaudhry, Mohammad S. Samman (2008)

Mathematica Bohemica

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We identify some situations where mappings related to left centralizers, derivations and generalized ( α , β ) -derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation T , of a semiprime ring R the mapping ψ R → R defined by ψ ( x ) = T ( x ) x - x T ( x ) for all x ∈ R is a free action. We also show that for a generalized ( α , β ) -derivation F of a semiprime ring R , with associated ( α , β ) -derivation d , a dependent element a of F is also a dependent element of α + d . Furthermore, we prove that for a centralizer...