Generalized Derivations with Power Central Values on Multilinear Polynomials on Right Ideals

Argaç, Nurcan; Filippis, Vincenzo De; Inceboz, Hulya G.

doi:10.4171/rsmup/120-4

Cited by 7 publications

(2 citation statements)

References 14 publications

(25 reference statements)

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“…Thus either β ji = 0 or β ji = 0. By (1) we have that either any sth column of λ(a) is zero, for any s ≤ p and s = j, or any sth column of µ(a) is zero, for any s ≤ p and s = j.…”

Section: The Case Of Inner Generalized Derivationsmentioning

confidence: 99%

Annihilators of Power Values of Generalized Derivations on Multilinear Polynomials

Filippis

2009

Bull. Aust. Math. Soc.

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Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, I a nonzero right ideal of R. Let f (x 1 , . . . , x n ) be a noncentral multilinear polynomial over C, m ≥ 1 a fixed integer, a a fixed element of R, g a generalized derivation of R. If ag( f (r 1 , . . . , r n )) m = 0 for all r 1 , . . . , r n ∈ I , then one of the following holds: (1) a I = ag(I ) = (0); (2) g(x) = q x, for some q ∈ U and aq I = 0;is an identity for I ; (4) g(x) = cx + [q, x] for all x ∈ R, where c, q ∈ U such that cI = 0 and [q, I ]I = 0.2000 Mathematics subject classification: primary 16N60, 16W25.

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“…Thus either β ji = 0 or β ji = 0. By (1) we have that either any sth column of λ(a) is zero, for any s ≤ p and s = j, or any sth column of µ(a) is zero, for any s ≤ p and s = j.…”

Section: The Case Of Inner Generalized Derivationsmentioning

confidence: 99%

Annihilators of Power Values of Generalized Derivations on Multilinear Polynomials

Filippis

2009

Bull. Aust. Math. Soc.

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“…Obviously any derivation is a generalized derivation. Moreover, another basic example of a generalized derivation is the mapping of the form g(x) = ax + xb for a, b ∈ R. Many authors have studied generalized derivations in the context of prime and semiprime rings (see [1], [2], [3], [13], [9], [18]). …”

Section: Introductionmentioning

confidence: 99%

A Result on Generalized Derivations With Engel Conditions on One-Sided Ideals

Demir¹,

Argaç²

2010

Journal of the Korean Mathematical Society

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Abstract. Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that [g(x m )x n , x r ] k = 0 for all x ∈ I, then there exists a ∈ U such that g(x) = xa for all x ∈ R except when R ∼ = M 2 (GF (2)) and I[I, I] = 0.

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Generalized Jordan Derivations on Semiprime Rings and Its Applications in Range Inclusion Problems

Wei

Xiao

2010

Mediterr. J. Math.

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It is shown that any generalized Jordan (triple-)derivation on a 2-torsion free semiprime ring is a generalized derivation and that any generalized Jordan higher derivation on a 2-torsion free semiprime ring is a generalized higher derivation. Then we give several conditions which enable some generalized Jordan derivations on prime rings to degenerate left or right multipliers. Lastly, we apply these degenerating conditions to discuss the range inclusion problems of generalized derivations on noncommutative Banach algebras.Mathematics Subject Classification (2010). Primary 16W25, 16N60; Secondary 47B47.

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Generalized Derivations with Power Central Values on Multilinear Polynomials on Right Ideals

Cited by 7 publications

References 14 publications

Annihilators of Power Values of Generalized Derivations on Multilinear Polynomials

Annihilators of Power Values of Generalized Derivations on Multilinear Polynomials

A Result on Generalized Derivations With Engel Conditions on One-Sided Ideals

Generalized Jordan Derivations on Semiprime Rings and Its Applications in Range Inclusion Problems

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