✦ LIBER ✦

A Class of Actions of Inverse Semigroups

✍ Scribed by Mark V. Lawson

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 310 KB
Volume: 179
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0025

No coin nor oath required. For personal study only.

✦ Synopsis

We generalise the classical Munn representation of an inverse semigroup with the introduction of what we call ordered representations of inverse semigroups. Both the Wagner᎐Preston Representation and the effective actions of O'Carroll and McAlister are examples of such representations. We show that every ordered representation of an inverse semigroup S determines and is determined by a special kind of cover of S. As applications, we provide a fully categorical account of the theory of idempotent pure congruences, and we show that every inverse semigroup which is a semilattice with respect to the natural partial ordering is an image of a combinatorial inverse semigroup under an L L-bijective, prehomomorphism.

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