On centralizers of prime gamma rings

Abstract EN

In this paper, we introduce some results in a prime Γ-ring M with centralizer which is related to the quotient Γ-ring Q of M, and prove our main result; Let Me be a prime Γ-ring with char M ≠ 2, U a non-zero right ideal of M and T1 and T2 two non-zero centralizers of M.

If T1T2 (U) = (0), then there exists two elements p, q of Q such that q ΓU = (0) and p ΓU = (0).