A Some Results on Double Cenralizer for Prime and Semiprime Г- rings

Abstract

The goal of this work, is to examine the concept of a double centralizer, and double Jordan centralizer on prime and semiprime Г-rings, this is done by studying examples, remarks and results related to that concepts and looking for the conditions under which T equal S, we prove the results, the first result, let A be a semiprime Γ-ring and T is a left centralizer, S is a right centralizer, and they fulfilling x T(y) = S (x) y, for each x A, Γ, thence (T,S) is a double centralizer. The second, let A be a prime Γ-ring, U be a not equal zero ideal of A, such that, T is a left centralizer, S is a right centralizer, and fulfilling x T(y) = S (x) y, for each x, y U, Γ, thence (T, S) is a double centralizer. The third, let A be a prime Γ-ring, U be a non-zero ideal of A, and we get , if T=S on U, thence T=S on A.

Keywords

• Keywords: Prime Г- rings , Semiprime Г- rings, centralizer, Jordan centralizer, double centralizer, double Jordan centralizer.