Three Approaches to Inverse Semigroups

Authors

  • Christopher Hollings Mathematical Institute, University of Oxford

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

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}.

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Published

2015-07-25

Issue

Vol. 8 No. 3: (July 2015)

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Three Approaches to Inverse Semigroups. (2015). European Journal of Pure and Applied Mathematics, 8(3), 294-323. https://www.ejpam.com/index.php/ejpam/article/view/2338