Three Approaches to Inverse Semigroups


  • Christopher Hollings Mathematical Institute, University of Oxford


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


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}.


How to Cite

Hollings, C. (2015). Three Approaches to Inverse Semigroups. European Journal of Pure and Applied Mathematics, 8(3), 294–323. Retrieved from