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Symmetric Bi-Centralizers on Semiprime Rings | ||
| Baghdad Science Journal | ||
| Article 1, Volume 12, Issue 4, 2015, Pages 838-845 | ||
| Authors | ||
| Eqbal J. Harjan; Auday H. Mahmood | ||
| Abstract | ||
| Let R be a 2-torsion free semiprime ring and F: R×R→ R be a symmetric Bi-additive mapping. The purpose of this paper is to prove the following results: (1) If F(x2, y)= F(x, y)x fulfilled for all x,y ∈R, then F is a symmetric left Bi-centralizer. (2) If F(xωx, y) = x F(ω, y) x fulfilled for all x,y, ω∈R, then F is a symmetric Bi-centralizer (3) Let R be a 2-torsion free semiprime ring with an identity element and F:R×R→ R be a symmetric Bi-additive mapping such that F(x3, y) = x F(x, y)x fulfilled for all x,y ∈R, then F is a symmetric Bi-centralizer | ||
| Keywords | ||
| Semiprime ring; A symmetric al left; centralizer; A symmetric al Jordan Bi | ||
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