Parcijalna uređenja određena uopštenim inverzima i anulatorima

The dissertation is a contribution in defining and studying different types of partial orders on rings, particularly on von Neumann regular and Rickart rings, as well as on the algebras of bounded operators on Banach and Hilbert spaces. In the first part of the dissertation, using generalized inverses of elements, the definitions of the minus, star, sharp, core and dual core partial orders are extended from the set of complex matrices to an arbitrary ring (with or without an involution). In a unified approach it is shown that the condition a