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 specically, 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.