G-outer inverses and partial orders in rings

The notions of G-outer inverse and its one-sided versions for rectangular complex matrices are generalized to elements of a ring based on the $(b,c)$-inverse. Various properties and characterizations of G-outer inverse and its one-sided kinds are developed. We consider partial orders applying G-outer inverse and its one-sided types in a ring. Consequently, one-sided G-Drazin inverses are introduced for elements of a ring as well as partial orders induced by them.