Some Results on Double Cenralizer for Prime and Semiprime Г- rings - Hussein, Aya; Majeed , Abdulrahman H.; Smeein , Shrooq Bahjat; Abu-Shams , Azza I.M.S. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2025)
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.