Some characterizations of rightc-regularity and(b;c)-inverse

Let R be a ring and a, b, c is an element of R. We give a novel characterization of group inverses (resp. EP elements) by the properties of right (resp. left ) c-regular inverses of a and discuss the relation among the strongly left (b, c)-invertibility of a, the right ca-regularity of b, and the (b, c)-invertibility of a. Finally, we investigate the sufficient and necessary condition for a ring to be a strongly left min-Abel ring by means of the (b, c)-inverse of a.