Generalized skew derivations as a generalization of left Jordan multipliers in prime rings

Abstract

Let m, n be two nonzero fixed positive integers, R a prime ring with the right Martindale quotient ring Q, G and H two generalized skew derivations of R with the same associated automorphism α of R. If $G(x^{m+n})=H(x^m)x^n$ is an identity for R, then either R is commutative or there exists $q\in Q$ such that $G(x)=H(x)=qx$, for any $x\in R$.

KEYWORDS:

• Generalized polynomial identity
• generalized skew derivation
• prime ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16R50
• 16W25
• 16N60