Annihilators of power values of derivations in prime rings

Chang, Chi‐Ming; Lee, Tsiu-Kwen

doi:10.1080/00927879808826263

Cited by 32 publications

(7 citation statements)

References 17 publications

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“…Chang and Lee [4] establish a unified version of the previous results for prime rings. Specifically, they prove the following theorem: let R be a prime ring, a nonzero right ideal of R, d a nonzero derivation of R, a ∈ R such that ad([x, y]) m ∈ Z (R) (d([x, y]) m a ∈ Z (R)).…”

Section: Introductionmentioning

confidence: 70%

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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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Section: Introductionmentioning

confidence: 70%

“…is trivial, that is, when either au = 0 or (α + b) = 0. Since au = 0 forces a contradiction, we get b = −α ∈ C and a(c + b)I = 0.If there exists γ ∈ C such that (c − γ )I = 0, by(4) it follows that(a f (ux 1 , . .…”

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confidence: 93%

Annihilators of Power Values of Generalized Derivations on Multilinear Polynomials

Filippis

2009

Bull. Aust. Math. Soc.

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“…This result of Posner was generalized in many directions by several authors and they studied the relationship between the structure of prime or semiprime ring and the behaviour of additive maps satisfying various conditions. Some authors have studied the derivations with annihilator conditions in prime and semiprime rings (see [3], [4], [6], [7], [8], [9]; where further references can be found).…”

Section: Introductionmentioning

confidence: 99%

Derivations With Annihilator Conditions in Prime Rings

Dhara¹,

Kar²,

Mondal³

2013

Bulletin of the Korean Mathematical Society

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“…In [8], C. M. Chang and T. K. Lee proved the following theorem: Let R be a prime ring, I a nonzero right ideal of R , d a nonzero derivation of R and a ∈ R be such that ad ([x, y]) m ∈ Z(R) (d([x, y]) m a ∈ Z(R)…”

Section: Introductionmentioning

confidence: 99%