An Orthogonal Left Centralizer and Reverse Left Centralizer on Semiprime -Rings
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Abstract
Let M be a semiprime G-ring . In this paper we introduce the concept of orthogonal left centralizer and reverse left centralizer on a semiprime G- ring and we prove the following main result: Let M be a 2-torsion free semiprime G- ring, t be a left centralizer and h be a reverse left centralizer of M , such that xazby = xbzay , for all x , y , z Î M , a , b Î G and t , h are commuting. Then t and h are orthogonal if and only if t(x) G M G h(y) + h(x) G M G t(y) = (0) , for all x , y Î M .
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