On (θ, φ)- Derivations on Lie Ideal of Semiprime Rings

EasyChair Preprint 6160

Abstract

Let R be a semiprime ring of characteristic ̸= 2 . Earlier the properties of Lie rings of derivations in commutative differentially prime rings R was investigated by many authors. In recent manuscript we find the conditions on semiprime rings R, when the left (θ, φ)-derivations is acting on Lie ideal of R. In particular we prove that if A is a nonzero Lie ideal and a subring of a characteristic ̸= 2 of a semiprime ring R and d is a (θ, φ)- derivation of R satisfaiying the condition d(ab) = d(ba)∀a, b ∈ A, then A ⊆ Z(R) and [R, R] ⊆ Z(R).

Keyphrases: Lie ideal, Prime ring, Semiprime ring, derivations

@booklet{EasyChair:6160,
  author    = {Iman Taha and Rohaidah Binti Masri and Rawdah Adawiyah Binti Termizi},
  title     = {On (θ, φ)- Derivations on Lie Ideal of Semiprime Rings},
  howpublished = {EasyChair Preprint 6160},
  year      = {EasyChair, 2021}}