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Some Results on (,) – Lie Ideals in Prime rings | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 48, Issue 1, 2007, Pages 166-171 | ||
| Authors | ||
| Abdul-Ruhman Hameed; Kassim Abdul-Hameed | ||
| Abstract | ||
| Let R be a prime with characteristic not equal two, σ,τ : R R be two automorphisms of R. and d be a nonzero derivation of R commuting with σ,τ .It is proved that : 1) Assume U ba a(σ,τ)-left Lie ideal of R. (a) If [U,U]s,t ÌCs,t and [U,U]=(0) ,then UÌZ(R). (b) If [U,U]s,t ÌCs,t , then UÌZ(R) . (c) If s(v)+t(v)ÏZ(R) , for some vÎU ,then there exists a nonzero left ideal A of R and a nonzero right ideal B of R such that [R,A]s,t ÌU , [R,B]s,tÌU but [R,A]s,tË Cσ, and [R,B]Ë Cσ, . (d) If for , then a=0 or s(u)+t(u)ÏZ(R) , for all uÎU. 2) If U be a(σ,τ)-Lie ideal of R for , , then a=0 or . Also, in this paper we study some results when characteristic of R equal two and we show that the condition characteristic of R not equal two can not be excluded. | ||
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