Partial orders in rings based on generalized inverses – unified theory

The unified theory for matrix partial orders based on generalized inverses has already been done by Mitra. We consider a special kind of ring R, which generalizes the ring of linear operators on finite dimensional vector space, and extend Mitra's approach to it. Thus, we find necessary and sufficient condition for a G-based relation to be a partial order on R. Also, some known results are generalized and some new results are proved.