Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-27T01:18:24.352Z Has data issue: false hasContentIssue false
  • English
  • Français

Retracts of trees and free left adequate semigroups

Part of: Algebraic structures Semigroups

Published online by Cambridge University Press:  17 August 2011

Mark Kambites
Mark Kambites
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK (mark.kambites@manchester.ac.uk)
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.

Recent research of the author has studied edge-labelled directed trees under a natural multiplication operation. The class of all such trees (with a fixed labelling alphabet) has an algebraic interpretation, as a free object in the class of adequate semigroups. We consider here a natural subclass of these trees, defined by placing a restriction on edge orientations, and show that the resulting algebraic structure is a free object in the class of left adequate semigroups. Through this correspondence we establish some structural and algorithmic properties of free left adequate semigroups and monoids, and consequently of the category of all left adequate semigroups.

Keywords

directed treeretractleft adequate semigroupfree algebraword problem

MSC classification

Secondary: 20M10: General structure theory 08A50: Word problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 731 - 747
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Branco, M. J. J., Gomes, G. M. S. and Gould, V. A. R., Structure of left adequate and left Ehresmann monoids, Int. J. Alg. Comput. (in press).Google Scholar
2.Cockett, J. R. B. and Guo, X., Stable meet semilattice fibrations and free restriction categories, Theory Applic. Categories 16(15) (2006), 307–341.Google Scholar
3.Cockett, J. R. B. and Lack, S., Restriction categories, I, Categories of partial maps, Theor. Comp. Sci. 270 (2002), 223–259.CrossRefGoogle Scholar
4.Cohn, P. M., Universal algebra, 2nd edn, Mathematics and Its Applications, Volume 6 (D. Reidel, Dordrecht, 1981).Google Scholar
5.Fountain, J. B., Adequate semigroups, Proc. Edinb. Math. Soc. 22 (1979), 113–125.Google Scholar
6.Fountain, J. B., Free right type A semigroups, Glasgow Math. J. 33 (1991), 135–148.CrossRefGoogle Scholar
7.Fountain, J. B., Gomes, G. M. S. and Gould, V. A. R., The free ample monoid, Int. J. Alg. Comput. 19(4) (2009), 527–554.Google Scholar
8.Gomes, G. M. S. and Gould, V. A. R., Left adequate and left Ehresmann monoids, II, preprint (available at www-users.york.ac.uk/~varg1/properadequatefinal.pdf).Google Scholar
9.Gould, V. A. R., (Weakly) left E-ample semigroups, preprint (available at www-users.york.ac.uk/~varg1/finitela.ps).Google Scholar
10.Kambites, M., Free adequate semigroups, J. Austral. Math. Soc. (in press).Google Scholar
11.Munn, W. D., Free inverse semigroups, Proc. Lond. Math. Soc. 29 (1974), 385–404.Google Scholar