Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-20T17:19:56.745Z Has data issue: false hasContentIssue false
  • English
  • Français

The 𝒥-classes of an inverse semigroup

Published online by Cambridge University Press:  09 April 2009

C. J. Ash
C. J. Ash
Affiliation:
Department of Mathematics Monash UniversityClayton, Victoria 3168, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown, using the author's construction for ‘labelled semilattices’, that every partially ordered set, in which every two elements have a common lower bound, is isomorphic to the partiallyordered set of 𝒥-classes of some completely semi-simple inverse semigroup.

1980 Mathematics subject classification (Amer. Math. Soc): primary 20 M 10, secondary 04 A 05, 08 A 05.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 427 - 432
Copyright
Copyright © Australian Mathematical Society 1979

References

Ash, C. J. (1979), ‘Uniform labelled semilattices’, J. Austral. Math. Soc, (Ser. A) 28, 385–397.CrossRefGoogle Scholar
Ash, C. J. and Hall, T. E. (1975), ‘Inverse semigroups on graphs’, Semigroup Forum11, 140–145.CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B. (1961 and 1967), ‘The algebraic theory of semigroups’, Math. Surveys of the American Math. Soc. (Providence, R.I., Vols 1 and 2).Google Scholar
Hall, T. E. (1973), ‘The partially ordered set of all 𝒥-classes of an inverse semigroup’, Semigroup Forum 6, 263–264.Google Scholar
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London), 92.Google Scholar
Munn, W. D. (1966), ‘Uniform semilattices and bisimple inverse semigroups’, Quart. J. Math.Oxford (2) 17, 151–159.CrossRefGoogle Scholar
Rhodes, J. (1972), ‘Research Problem 24’, Semigroup Forum 5.Google Scholar