b′-Generalized skew derivations acting as a Jordan derivation on multilinear polynomials in prime rings

Abstract

Let R be a prime ring of characteristic not equal to 2, U the Utumi quotient ring of R, C the extended centroid of R and $f(x_1,\dots ,x_n)$ a noncentral multilinear polynomial of R. Let F, H be $b^{\prime }$-generalized skew derivations on R, with associated terms $(b\prime ,\alpha ,d)$ and $(b\prime ,\alpha ,\delta )$ respectively, and α commutes with d and δ. In this article we study the complete structure of F and H in the case $F(u)u+uF(u)=H(u^2)$, for all $u=f(r_1,\dots ,r_n),r_1,r_2,\dots ,r_n\in R$.

Keywords:

• b-Generalized skew derivations
• extended centroid
• multilinear polynomials
• Utumi quotient ring

Mathematics Subject Classification 2020:

• 16N60
• 16W25

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.