Hostname: page-component-6bf8c574d5-pdxrj Total loading time: 0 Render date: 2025-03-08T15:53:06.285Z Has data issue: false hasContentIssue false
  • English
  • Français

A coordinatisation of implicative (semi-)lattices by Baer semigroups*

Published online by Cambridge University Press:  14 November 2011

T. S. Blyth
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
Get access Rights & Permissions [Opens in a new window]

Synopsis

We show that if L is a bounded (semi-)lattice and f is a range-closed idempotent residuated mapping on L then f is multiplicative if and only if it is decreasing. We then use this to prove that a bounded (semi-)lattice is implicative if and only if it can be coordinatised by a weakly multiplicative (right) Baer semigroup.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 111 - 113
Copyright
Copyright © Royal Society of Edinburgh 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Blyth, T. S. and Janowitz, M. F.. Residuation theory (Oxford: Pergamon Press. 1972).Google Scholar
2Janowitz, M. F.. Decreasing Baer semigroups. Glasgow Math. J. 10 (1969) 46–41.CrossRefGoogle Scholar
3Johnson, C. S.. Semigroups coordinatising posets and semilattices. J. London Math. Soc. 4 (1971) 277–283.CrossRefGoogle Scholar