Abstract
We discuss the result that every finite semigroup in which idempotents commute is a homomorphic image of a sub-semigroup of some finite inverse semigroup. The full proof of the general result is to appear elsewhere In this paper we describe in detail the special case where the relation I is trivial. This contains most of the features of the general case and we outline what modifications are needed for this.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ash, C.J., ‘Finite semigroups with commuting idempotents’. J. Aust. Math. Soc. (to appear).
Margolis, S.W. ‘Problem 14’, Proceedings of the Nebraska conference on semigroups, (Ed. J. Meakin), September 1980, p. 14.
Margolis, S.W. and Pin, J.E. ‘Languages and inverse semigroups’. 11th ICALP, Lecture Notes in Computer Science 172 (1984), 337–346.
Margolis, S.W. and Pin, J.E. ‘Graphs, inverse semigroups and languages’. Proceedings of the 1.984 Marquette conference on semigroups. Marquette University (1984), 85–112.
Pin, J.E. Variétés de langages formels. Masson, Paris (1984).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company
About this chapter
Cite this chapter
Ash, C.J. (1987). Finite Idempotent-Commuting Semigroups. In: Goberstein, S.M., Higgins, P.M. (eds) Semigroups and Their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3839-7_2
Download citation
DOI: https://doi.org/10.1007/978-94-009-3839-7_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8209-9
Online ISBN: 978-94-009-3839-7
eBook Packages: Springer Book Archive