An Engel condition with b-generalized derivations

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Abstract

Let R be a noncommutative prime ring with the extended centroid C, I a nonzero ideal of R and g a b-generalized derivation of R. We show that, if [g(xm), xn]=0 for all x ϵ I, where m, n, k are fixed positive integers, then there exists ϵ λ C such that g(x) for all xϵR unless R ≅ M2(GF(2)), the 2x2 matrix ring over the Galois field GF(2) of two elements. This gives a natural generalization of the results for derivations, generalized derivations and generalized σ -derivations with an X-inner automorphism σ.

Original languageEnglish
Pages (from-to)300-312
Number of pages13
JournalLinear and Multilinear Algebra
Volume65
Issue number2
DOIs
Publication statusPublished - 2017 Feb 1

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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