![]() |
Department of Mathematics
|
Rings and Modules Seminar
|
---|
Kenneth Onuma
onumak(at)myumanitoba(dot)ca
University of Manitoba
Tuesday, November 14, 2017
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': y∈S such that y∈bSy , y∈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. |