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XII.—Quasi-residuated Mappings and 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

We consider, for a given ordered set E with minimum element O, the semigroup Q of O-preserving isotone mappings on E and examine necessary and sufficient conditions under which an element fε Q is such that the left [resp. right] annihilator of f in Q is a principal left [resp. right] ideal of Q generated by a particular type of idempotent. The results obtained lead us to introduce the concept of a Baer assembly which we use to extend to the case of a semilattice the Baer semigroup co-ordinatization theory of lattices. We also derive a co-ordinatization of particular types of semilattice.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 2 , 1971 , pp. 165 - 179
Copyright
Copyright © Royal Society of Edinburgh 1971

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References

References to Literature

[1]Janowitz, M. F., 1965. “Baer semigroups”, Duke Math. J., 32, 83–96.CrossRefGoogle Scholar
[2]Janowitz, M. F., 1966. “A semigroup approach to lattices”, Can.J. Math., 18, 1212–1223.CrossRefGoogle Scholar
[3]Blyth, T. S., and Janowitz, M. F.Residuation Theory. Pergamon Press (to appear).Google Scholar