Generalized skew-derivations and generalization of homomorphism maps in prime rings

Abstract

Let R be a noncommutative prime ring of characteristic different from 2, Q_r the right Martindale quotient ring of R, $C=Z(Q_r)$ the extended centroid of R and $f(x_1,\dots ,x_n)$ a noncentral multilinear polynomial over C. In this paper we describe all possible forms of two generalized skew derivations F and G of R satisfying the condition $F{(u)}^2=G(u^2)$, for all $u\in f(R)$.

Keywords:

• Derivation
• generalized derivation
• generalized skew derivation
• prime ring

2010 MATHEMATICAL SUBJECT CLASSIFICATION:

• Primary: 16W25
• Secondary: 16N60
• 16R50

Additional information

Funding

Basudeb Dhara is supported by a grant from Science and Engineering Research Board (SERB), DST, New Delhi, India. Grant no. is EMR/2016/004043 dated 29 November 2016.