Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-26T15:17:30.675Z Has data issue: false hasContentIssue false
  • English
  • Français

0-Distributive and P-Uniform Semilattices

Published online by Cambridge University Press:  20 November 2018

C. S. Hoo  and
K. P. Shum
C. S. Hoo
Affiliation:
University of Alberta, Edmonton, Alberta, Canada
K. P. Shum
Affiliation:
Chinese University of Hong Kong, Shatin, N.T. Hong Kong
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.

A counter-example is provided to the conjecture of Y. S. Pawar and N. K. Thakare that a semilattice S with 0 is 0-distributive if and only if for each filter F and each ideal I such that F ∩ I = Ø, there exists a prime filter containing F and disjoint from I. This shows that 0-distributivity is not equivalent to weak distributivity. A characterization is also given of finite P-uniform semilattices in terms of 0-distributivity.

Keywords

06A1206D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 317 - 324
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Balbes, R., A representation theory for prime and implicative semilattices. Trans. Amer. Math. Soc. 136 (1969) 261-267.Google Scholar
2. Grätzer, G., Universal Algebra. D. Van Nostrand Co., Princeton, 1968.Google Scholar
3. Numakura, K., Prime ideals and idempotents in compact semigroups. Duke Math. J. 24 (1957) 671-679.Google Scholar
4. Paalman-de Miranda, A. B., Topological semigroups. Mathematical Centre Tracts, Amsterdam 1964.Google Scholar
5. Pawar, Y. S. and Thakare, N. K., 0-distributive semilattices. Can. Math. Bull. 21(1978) 469-475.Google Scholar
6. Shoji, K. and Yamada, M., D*-simple inverse semigroups. Symposium on semigroup theory, Shimane, Japan 1977, pages 13-28.Google Scholar
7. Varlet, J. C., Relative annihilators in semilattices. Bull. Austral. Math. Soc. 9 (1973) 169-185.Google Scholar
8. Venkatanarasimhan, P. V., Stone's topology for pseudocomplemented and bicomplemented lattices. Trans. Amer. Math. Soc. 170 (1972) 57-70.Google Scholar