Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T01:08:04.986Z Has data issue: false hasContentIssue false
  • English
  • Français

Classes of Semilattices Associated with an Equational Class of Lattices

Published online by Cambridge University Press:  20 November 2018

H. S. Gaskill
H. S. Gaskill*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper we consider the question of whether there is a natural class of semilattices associated with a fixed equational class of lattices. We give four classes of semilattices which may be obtained from a given equational class of lattices and show that for the distributive case they coalesce into one class. An incomplete set of relations is given for the general case.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 361 - 365
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Birkhoff, G., Lattice theory (Amer. Math. Soc. Colloquim Publications, XXV, Providence, R.I., 1967).Google Scholar
2. Grätzer, G., Universal algebra (D. Van Nostrand Company, Inc., Toronto, 1968).Google Scholar
3. Green, C., Distributive semilattices, Notices Amer. Math. Soc. 15 (1968), 68T-A55.Google Scholar
4. Rhodes, J. B., Modular semilattices, Notices Amer. Math. Soc. 17 (1970), 672–679.Google Scholar