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Displaying similar documents to “On left ( θ , ϕ ) -derivations of prime rings”

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 .

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.

Derivations with Engel conditions in prime and semiprime rings

Shuliang Huang (2011)

Czechoslovak Mathematical Journal

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Let R be a prime ring, I a nonzero ideal of R , d a derivation of R and m , n fixed positive integers. (i) If ( d [ x , y ] ) m = [ x , y ] n for all x , y ∈ I , then R is commutative. (ii) If Char R ≠ 2 and [ d ( x ) , d ( y ) ] m = [ x , y ] n for all x , y ∈ I , then R is commutative. Moreover, we also examine the case when R is a semiprime ring.