μ-Centralizers with Commutativity Results of Prime and Semiprime Γ-Rings

Authors

  • Maalim Salam Ahmad Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Abdulrahman H. Majeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.2.12

Keywords:

Prime rings, Semiprime rings, Centralizers, μ-Centralizers, Lie ideals

Abstract

 Let A be a 2- torsion free prime Γ- ring, and L be a square closed Lie ideal of A i.e. xβx∈L for all x∈L and β∈Γ, suppose that  μ is an endomorphism of A, and  f  is a right μ- centralizer which is not the identity map on L, satisfying f([x, b]_γ )=〖∓[x,b]〗_γ ( or f(xδr)=∓xδr)  for all x,b∈L , γ∈Γ, then L⊆Z(A).

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