Derivations with Engel and annihilator conditions on multilinear polynomials

Cheng Kai Liu

Research output: Contribution to journal › Article

11 Citations (Scopus)

Abstract

Let R be a prime ring with a nonzero derivation d and let f (X 1,...,Xt) be a multilinear polynomial over C, the extended centroid of R. Suppose that b[d(f(x1,...,xt)), f(x1,...,xt)]n = 0 for all xi ∈ R, where 0 ≠ b ∈ R and n is a fixed positive integer. Then f(X1,..., Xt) is centrally valued on R unless char R = 2 and dimC RC = 4. We prove a more generalized version by replacing R with a left ideal.

Original languageEnglish
Pages (from-to)719-725
Number of pages7
JournalCommunications in Algebra
Volume33
Issue number3
DOIs
Publication statusPublished - 2005 Dec 5

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Extended Centroid
Prime Ring
Annihilator
Polynomial
Integer

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Liu, Cheng Kai. / Derivations with Engel and annihilator conditions on multilinear polynomials. In: Communications in Algebra. 2005 ; Vol. 33, No. 3. pp. 719-725.
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Liu, CK 2005, 'Derivations with Engel and annihilator conditions on multilinear polynomials', Communications in Algebra, vol. 33, no. 3, pp. 719-725. https://doi.org/10.1081/AGB-200049880

Derivations with Engel and annihilator conditions on multilinear polynomials. / Liu, Cheng Kai.

In: Communications in Algebra, Vol. 33, No. 3, 05.12.2005, p. 719-725.

Research output: Contribution to journal › Article

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AU - Liu, Cheng Kai

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N2 - Let R be a prime ring with a nonzero derivation d and let f (X 1,...,Xt) be a multilinear polynomial over C, the extended centroid of R. Suppose that b[d(f(x1,...,xt)), f(x1,...,xt)]n = 0 for all xi ∈ R, where 0 ≠ b ∈ R and n is a fixed positive integer. Then f(X1,..., Xt) is centrally valued on R unless char R = 2 and dimC RC = 4. We prove a more generalized version by replacing R with a left ideal.

AB - Let R be a prime ring with a nonzero derivation d and let f (X 1,...,Xt) be a multilinear polynomial over C, the extended centroid of R. Suppose that b[d(f(x1,...,xt)), f(x1,...,xt)]n = 0 for all xi ∈ R, where 0 ≠ b ∈ R and n is a fixed positive integer. Then f(X1,..., Xt) is centrally valued on R unless char R = 2 and dimC RC = 4. We prove a more generalized version by replacing R with a left ideal.

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Liu CK. Derivations with Engel and annihilator conditions on multilinear polynomials. Communications in Algebra. 2005 Dec 5;33(3):719-725. https://doi.org/10.1081/AGB-200049880

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