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GRAPH PRODUCTS OF RIGHT CANCELLATIVE MONOIDS

Part of: Semigroups

Published online by Cambridge University Press:  09 October 2009

JOHN FOUNTAIN  and
MARK KAMBITES
JOHN FOUNTAIN*
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK (email: [email protected])
MARK KAMBITES
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull of such a graph product. We then specialize to the case of the inverse hulls of graph monoids, obtaining what we call ‘polygraph monoids’. Among other properties, we observe that polygraph monoids are F*-inverse. This follows from a general characterization of those right cancellative monoids with inverse hulls that are F*-inverse.

Keywords

graph productright cancellative monoidgraph monoidinverse hullF*-inverse monoid

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 227 - 252
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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