Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-13T09:54:37.611Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

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]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