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Rings and Modules Seminar
~ Abstracts ~

Kenneth Onuma
onumak(at)myumanitoba(dot)ca

University of Manitoba

Tuesday, November 14, 2017

Left and right generalized inverses
Abstract:

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': yS such that ybSy , yySc, 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.


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