Open AccessSome Results On Lie Ideals With (σ,τ)-derivationIn Prime Rings
Author(s) -
Baghdad Science Journal
Publication year - 2009
Publication title -
mağallaẗ baġdād li-l-ʿulūm
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.167
H-Index - 6
eISSN - 2411-7986
pISSN - 2078-8665
DOI - 10.21123/bsj.6.1.231-234
Subject(s) - mathematics , commutative ring , homomorphism , prime (order theory) , commutative property , combinatorics , ring (chemistry) , ideal (ethics) , discrete mathematics , chemistry , philosophy , epistemology , organic chemistry
In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative.(ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative.(iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.