Department of Mathematics
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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 \(b=c\).