in this paper, the orthomorphisms on the archimedean riesz space r " with the usual coordinatewise ordering are characterized . also, the direct sum decomposition of an order bounded operator with respect to the orthomorphisms is obtained 本文首先刻畫了n維歐氏空間r~n按通常的偏序做成的阿基米德riesz空間上正交射的特征,以此可對r~n上序有界算子作關于正交射的直和分解。