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GRAPH PRODUCTS OF RIGHT CANCELLATIVE MONOIDS

  • JOHN FOUNTAIN (a1) and MARK KAMBITES (a2)
Abstract

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.

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Copyright
Corresponding author
For correspondence; e-mail: jbf1@york.ac.uk
References
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Journal of the Australian Mathematical Society
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  • EISSN: 1446-8107
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