Some new characterizations of (b,c)-inverses and Bott-Duffin (e,f)-inverses

Abstract

The (b,c)-inverse and the Bott-Duffin (e,f)-inverse are two classes of outer inverses, a few characterizations of which have been presented by certain researchers. In this paper, we give some new characterizations of (b, c)-inverses and Bott-Duffin (e,f)-inverses. First, we present a number of ring theoretic characterizations of (b,c)-inverses. Then we characterize (b, c)-inverses by equations. Finally, we present some characterizations of Bott-Duffin (e,f)-inverses. More specifically, we use Bott-Duffin (e,f)- inverses to characterize some classes of rings, such as directly finite rings, Abelian rings and left min-abel rings.