Department of Mathematics
Server

In any semigroup $S$ or $*$-semigroup $S$, the Moore-Penrose inverse $y=a^+$, Drazin's pseudo-inverse $y=a'$, Chipman's weighted inverse and the Bott-Duffin inverses are all special cases of the more general class of '$(b,c)$-inverses': $y\in S$ such that $y\in bSy$ , $y\in ySc$, $yab=b$ and $cay=c$. The concept of $(b,c)$-inverses was originally introduced by M.P. Drazin in 2012.

In this talk, we shall examine a way to define left and right versions of the large class of $(b,c)$-inverses and discuss their basic properties. Similar to ordinary left and right inverses, we shall discuss a way to extend the so-called Dedekind finiteness conditions to left and right $(b,c)$-inverses in the special case when $b=c$.