A note on derivations and Jordan ideals of prime rings

AIMS Mathematics

关键词: : ;    Prime rings;    Jordan ideals;    Generalized derivations;    Martindale ring of quotients;    Generalized polynomial identities (GPIs);   

DOI  :  10.3934/Math.2017.4.580

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

Let F : R → R be a generalized derivation of a 2-torsion free prime ring R together witha derivation d: In this paper, we show that a nonzero Jordan ideal J of R contains a nonzero ideal ofR. Further, we use this result to prove that if F([x,y]) ∈ Z(R) for all x, y ∈ J; then R is commutative.Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.

【 授权许可】

CC BY