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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.
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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

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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