Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-19T03:44:03.399Z Has data issue: false hasContentIssue false
  • English
  • Français

Congruences on free monoids and submonoids of polycyclic monoids

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

John Meakin  and
Mark Sapir
John Meakin
Affiliation:
Department of Mathematics and StatisticsUniversity of Nebraska-LincolnLincoln, Nebraska 68588-0323, U.S.A.
Mark Sapir
Affiliation:
Department of Mathematics and StatisticsUniversity of Nebraska-LincolnLincoln, Nebraska 68588-0323, U.S.A.
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.

We establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 2 , April 1993 , pp. 236 - 253
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Adian, S. I., ‘Defining relations and algorithmic problems for groups and semigroups’, Trudy Mat. Inst. Steldov 85 (in Russian) Am. Math. Soc. translation 152, 1967.Google Scholar
[2]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys Monographs 7, vol. 1, vol. 2 (Amer. Math. Soc., Providence, 1961–1967).Google Scholar
[3]Lyapin, E. S., Semigroups (Moscow, 1960) (in Russian).Google Scholar
[4]Margolis, S. and Meakin, J., ‘Inverse monoids, trees and context-free languages’, Trans. Amer. Math. Soc. (to appear).Google Scholar
[5]Matiyasevich, Yu. V., ‘Investigation on some algorithmic problems in algebra and number theory’, Trudy MIAN SSSR, 168 (1984), 218–235.Google Scholar
[6]Nivat, M., ‘Sur les automates a memoire pile’, in: Proceedings of the International Computing Symposium, Bonn, 1970 (ed. Itzeld, W.), (North Holland, Amsterdam, 1970) pp. 655–663.Google Scholar
[7]Nivat, M. and Perrot, J. F., ‘Une generalisation du monoide bicyclique’, C.R. Acad. Sci. Paris Sér. I Math. A 271 (1970), 824–827.Google Scholar
[8]Petrich, M., Inverse semigroups, (Wiley, New York, 1984).Google Scholar
[9]Sakarovitch, J., Syntaxe des langages de Chomsky, (Th. Sc. Math., Univ. Paris 7, 1979).Google Scholar
[10]Stephen, J., ‘Presentations of inverse monoids’, J. Pure and Applied Algebra 63 (1990), 81–112.CrossRefGoogle Scholar
[11]Whaley, Th. P., Algebras satisfying the descending chain condition for subalgebras, (Ph.D. Thesis, Vanderbilt University, 1968).Google Scholar