Three Approaches to Inverse Semigroups

Christopher Hollings

Abstract

I give a historical survey of the three main approaches to the study of the structure of inverse semigroups.  The first is that via \emph{inductive groupoids}, as studied by Charles Ehresmann.  The second concerns the notion of a \emph{fundamental} inverse semigroup and its \emph{Munn representation}.  Finally, the third centres upon the concept of an \emph{$E$-unitary} or \emph{proper} inverse semigroup and its representation (due to McAlister) by a so-called \emph{$P$-semigroup}.

Keywords

inverse semigroup (fundamental, $E$-unitary, proper), inductive groupoid, idempotent-separating congruence, Munn representation, $E$-unitary cover, minimum group congruence, maximum group image, $P$-semigroup, $P$-theorem

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