Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T05:24:27.524Z Has data issue: false hasContentIssue false
  • English
  • Français

The Macneille Completion of a Uniquely Complemented Lattice

Published online by Cambridge University Press:  20 November 2018

John Harding
John Harding*
Affiliation:
Department of Mathematics, Vanderbilt University Nashville, Tennessee 37240 U.S.A.
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.

Problem 36 of the third edition of Birkhoff's Lattice theory [2] asks whether the MacNeille completion of uniquely complemented lattice is necessarily uniquely complemented. We show that the MacNeille completion of a uniquely complemented lattice need not be complemented.

Keywords

06C1506A23
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 222 - 227
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Adams, M. E., Uniquely complemented lattices. In: The Dilworth theorems: selected papers of Robert P. Dilworth, (eds. Bogart, Freese and Kung), Birkhauser, 1990,79–84.Google Scholar
2. Birkhoff, G., Lattice theory, Third éd., Amer. Math. Soc. Coll. Publ. XXV, Providence, 1967.Google Scholar
3. Dilworth, R. P., Lattices with unique complements, Trans. Amer. Math. Soc. 57(1945), 123–154.Google Scholar
4. Glavin, F. and B. Jônsson, Distributive sublattices of a free lattice, Canad. J. Math. 13(1961), 265–272.Google Scholar
5. MacNeille, H. M., Partially ordered sets, Trans. Amer. Math. Soc. 42(1937), 416–460.Google Scholar
6. Saliï, V. N., Lattices with unique complements, Translations of the Amer. Math. Soc, Providence, 1988.Google Scholar
7. Whitman, P. M., Free latticesAnn. of Math. 42(1941), 325–330.Google Scholar
8. Whitman, P. M., Free lattices II, Ann. of Math. 43(1942), 104–115.Google Scholar