Generalized derivations on Lie ideals in prime rings

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.

Anahtar Kelimeler:

Derivations, Lie ideals, generalized derivations, centralizing mappings, prime rings

Generalized derivations on Lie ideals in prime rings

Keywords:

Derivations, Lie ideals, generalized derivations, centralizing mappings, prime rings,

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Oznur G ¨OLBAS¸I and Emine KOC¸ Cumhuriyet University, Department of Mathematics , Sivas-TURKEY e-mail: ogolbasi@cumhuriyet.edu.tr e-mail: eminekoc@cumhuriyet.edu.tr