An Orthogonal Left Centralizer and Reverse Left Centralizer on Semiprime -Rings

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Fawaz Ra'ad Jarullah , Yilmaz Çeven

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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How to Cite
Fawaz Ra’ad Jarullah , Yilmaz Çeven. (2022). An Orthogonal Left Centralizer and Reverse Left Centralizer on Semiprime -Rings. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 13(2), 1035–1043. https://doi.org/10.17762/turcomat.v13i2.12673
Section
Research Articles