A quadratic generalized differential identity on Lie ideals of Prime Rings

ABSTRACT

Let R be a prime ring of characteristic different from 2, C its extended centroid and L a non-central Lie ideal of R. If $F:R\to R$ and $G:R\to R$ are two non-zero generalized derivations of R such that $\left[F\right(u),G(u\left)\right]=0$ for all $u\in L$, then $G=\lambda F$ for some $\lambda \in C$ except possibly when R satisfies the standard identity $s_4$ of degree 4.

COMMUNICATED BY:

• W.-F. Ke

KEYWORDS:

• Generalized polynomial identity
• generalized derivation
• prime and semiprime ring

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 16R50
• 16W25
• 16N60

Disclosure statement

No potential conflict of interest was reported by the authors.