Representations of the (b, c)-Inverses in Rings with Involution

Abstract

Let R be a ring and b, and c in R. The concept of (b; c)-inverses was introduced by Drazin in 2012. In this paper, necessary and sucient conditions for the existence of the (b; c)-inverse in a ring with an involution are investigated, and new expressions for them are derived. A new representation of the (b; c)-inverse based on the group inverse is also presented.