Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-30T23:52:13.350Z Has data issue: false hasContentIssue false
  • English
  • Français

XX.—A Coördinatisation of Lattices by One-sided Baer Assemblies

Published online by Cambridge University Press:  14 February 2012

T. S. Blyth  and
W. C. Hardy
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
W. C. Hardy
Affiliation:
Centre for Naval Analyses, Arlington, Virginia.
Get access Rights & Permissions [Opens in a new window]

Synopsis

In an earlier publication [1] we introduced the notion of a Baer assembly and applied it to obtain a coördinatisation theory for semilattices. This was achieved by considering the semigroup of quasi-residuated (i.e. ℴ-preserving and isotone) mappings on a bounded semilattice. In the present paper we consider the semigroup of quasi-residuated ∪-homomorphisms (or hemimorphisms) on a bounded lattice and thus show how a particular type of one-sided Baer assembly can be used to provide a coördinatisation theory for lattices; and in particular for complemented, modular and distributive lattices.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 4 , 1972 , pp. 267 - 279
Copyright
Copyright © Royal Society of Edinburgh 1972

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

References to Literature

[1]Blyth, T. S. and Hardy, W. C., 1971. ‘Quasi-residuated mappings and Baer assemblies’, Proc. Roy. Soc. Edinb., 69A, 165–179.Google Scholar