Compositions, derivations and polynomials

Xiaowei Xu (), Jing Ma () and Fengwen Niu ()
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Xiaowei Xu: Jilin University
Jing Ma: Jilin University
Fengwen Niu: Jilin University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 4, 543-556

Abstract: Abstract Let R be a prime ring with extended centroid C. In this paper, we discuss the case when the composition of a generalized derivation δ and a polynomial map f(Y) ∈ C[Y] of R is commutative on a non-zero right ideal ρ and a non-commutative Lie ideal L of R respectively, i.e., when the identity δ ○ f(x) = f ○ δ(x) holds on ρ or L. As applications of our main theorems, we clarify the generalized derivations which act as n-Jordan homomorphisms (S n -homomorphisms) on ρ or L.

Keywords: Prime ring; generalized derivation, polynomial, S n -homomorphism, n-Jordan homomorphism (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0029-4

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