
The main object of this paper is prove that: Let R be a 2-torsion free semiprime ring ,T=(Ti)iN and H=(Hi)iN be two generalized higher reverse left (resp. right) centralizers associated with the higher reverse left (resp. right) centralizers t=(ti)iN and h=(hi)iN resp. of R , where Tn and Hn are commuting. Then Tn and Hn are orthogonal if and only if Tn(x) Hn(y) = tn(x) Hn(y) = 0, for all x , y R and n N.