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Let R be a ∗−prime ring with characteristic not 2, U a nonzero ∗− (σ,τ)−Lie ideal of R, d a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τd = dτ and ∗ commutes with σ, τ, d. In the present paper it is... more
Let R be a ∗−prime ring with characteristic not 2, U a nonzero ∗− (σ,τ)−Lie ideal of R, d a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τd = dτ and ∗ commutes with σ, τ, d. In the present paper it is shown that if d(U) ⊆ Z or d2(U) ⊆ Z, then U ⊆ Z.
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This paper abstracts some results of M. Bresar and J. Vukman [1] on the orthogonal derivations of semiprime rings to (σ, τ)-derivations and generalized (σ, τ)-derivations.
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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... more
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.
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We extend some well known commutativity results concerning a nonzero square closed∗-Lie ideal and generalizedα,β-derivations of∗-prime rings.
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Let be a prime ring with 6 =2 and let be auto- morphisms of An additive mapping : → is called a generalized ( )−derivation if there exists a ( )−derivation : → such that ( )= ()( )+ ()() holds... more
Let be a prime ring with 6 =2 and let be auto- morphisms of An additive mapping : → is called a generalized ( )−derivation if there exists a ( )−derivation : → such that ( )= ()( )+ ()() holds for all ∈ In this paper
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Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a ∈ R and [a, f(U)] = 0 then a ∈ Z or d(a) = 0... more
Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a ∈ R and [a, f(U)] = 0 then a ∈ Z or d(a) = 0 or U ⊂ Z; (ii) If f
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Siberian Mathematical Journal, Vol. 48, No. 6, pp. 979983, 2007 Original Russian Text Copyright c 2007 Gölbasi ¨O. and Aydin N. ... ORTHOGONAL GENERALIZED (σ, τ)-DERIVATIONS OF SEMIPRIME RINGS ... Abstract: This paper abstracts some... more
Siberian Mathematical Journal, Vol. 48, No. 6, pp. 979983, 2007 Original Russian Text Copyright c 2007 Gölbasi ¨O. and Aydin N. ... ORTHOGONAL GENERALIZED (σ, τ)-DERIVATIONS OF SEMIPRIME RINGS ... Abstract: This paper abstracts some results of M. Bresar and J. ...
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ABSTRACT Let R be a 2-torsion free semiprime *-ring, σ, τ two epimorphisms of R and f, d : R → R two additive mappings. In this paper we prove the following results: (i) d is a Jordan (σ, τ)*-derivation if and only if d is a Jordan triple... more
ABSTRACT Let R be a 2-torsion free semiprime *-ring, σ, τ two epimorphisms of R and f, d : R → R two additive mappings. In this paper we prove the following results: (i) d is a Jordan (σ, τ)*-derivation if and only if d is a Jordan triple (σ, τ)*-derivation. (ii) f is a generalized Jordan (σ, τ)*-derivation if and only if f is a generalized Jordan triple (σ, τ)*-derivation.