Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T09:59:20.534Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the coordinatisation of implicative (semi-)lattices by Baer semigroups

Published online by Cambridge University Press:  14 November 2011

C. S. Johnson Jr.
C. S. Johnson Jr.
Affiliation:
Bowling Green State University, Ohio, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

We show that a bounded (semi-)lattice is implicative if and only if it can be coordinatised by a (right) Baer semigroup ℛS in which each element of (S) has an idempotent generator f such that fe = efe for all idempotents e with eS ∈ ℛ(S).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 115 - 116
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.. A coordinatisation of implicative (semi-) lattices by Baer semigroups. Proc. Roy. Soc. Edinburgh Sect. A 82 (1978), 111–113.Google Scholar
2Janowitz, M. F.. Semimultiplicative residuated mappings. Algebra Universalis 5 (1975), 429–442.Google Scholar
3Johnson, C. S. Jr, UIG Baer semigroups. J. Natur. Sci. and Math. 12 (1972), 287–295.Google Scholar