Abstract
A semilattice E is said to be a countable universal semilattice if E is countable and if every countable semilattice can be embedded in E. The free Boolean algebra on a countably infinite number of generators is used to construct a particular countable universal semilattice which is the semilattice of idempotents of a 2-generated bisimple monoid.
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
J. L. Bell and A. B. Slomson, Models and ultraproducts: an introduction, North Holland, Amsterdam, 1971.
K. Byleen, ‘Embedding any countable semigroup in a 2-generated bisimple monoid’, Glasgow Math. J. 25 (1984), 153–161.
T. E. Hall, ‘Inverse and regular semigroups and amalgamation: a brief survey’, Proceedings of a Symposium on Regular Semi-Groups, Northern Illinois University, 1979.
T. Imaoka, ‘Free products with amalgamation of bands’, Mem. Fac. Lit. & Sci., Shimane Univ., Nat. Sci. 10 (1976), 7–17.
B. Jónsson, universal relational systems’, Math. Scand. 4 (1956), 193–208.
B. Jónsson, ‘Homogeneous universal relational systems’, Math. Scand. 8 (1960), 137–142.
B. H. Neumann, ‘Some remarks on infinite groups’, J. London Math. Soc. 12 (1937), 120–127.
M. Petrich, Inverse Semigroups, Wiley, New York, 1984.
N. R. Reilly, ‘Embedding inverse semigroups in bisimple inverse semigroups’, Quart. J. Math., Oxford (2) 16 (1965), 183–187.
R. Sikorski, Boolean algebras, Springer-Verlag, Berlin, 1964.
S. Willard, General topology, Addison-Wesley, Reading, 1970.
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
Byleen, K. (1987). Inverse Semigroups with Countable Universal Semilattices. In: Goberstein, S.M., Higgins, P.M. (eds) Semigroups and Their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3839-7_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-3839-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8209-9
Online ISBN: 978-94-009-3839-7
eBook Packages: Springer Book Archive