Abstract
A chain (that is, a linear ordering) is said to be uniform if all of its principal ideals are isomorphic. A chain is scattered if it does not contain a subchain which is isomorphic to the chain of the rational numbers. We shall construct a class of pairwise non-isomorphic scattered uniform chains.
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
A. Clement and F. Pastijn, Inverse semigroups with idempotents dually well-ordered, J. Austral. Math. Soc. (A) 35 (1983), 373–385.
J.W. Hogan, Bisimple semigroups with idempotents well-ordered, Semigroup Forum 6 (1973), 298–316.
A.C. Morel, A class of relation types isomorphic to the ordinals, Mich. Math. J. 12 (1965), 203–215.
W.D. Munn, Fundamental inverse semigroups, Quart. J. Math. Oxford (2) 21 (1970), 157–170.
F. Pastijn, Scattered uniform chains, preprint.
J.G. Rosenstein, Linear Orderings, Academic Press, New York, 1982.
G.L. White, The dual ordinal of a bisimple inverse semigroup, Semigroup Forum 6 (1973), 295–297.
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
Pastijn, F. (1987). A Class of Uniform Chains. In: Goberstein, S.M., Higgins, P.M. (eds) Semigroups and Their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3839-7_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-3839-7_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8209-9
Online ISBN: 978-94-009-3839-7
eBook Packages: Springer Book Archive