Quasi-Residuated Mappings and Baer Assemblies.

Abstract

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 in which point f belongs to set 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 coordinatisation theory of lattices. We also derive a coordinatisation of particular types of semilattice. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 14, 1970
Accession Number
ADA071317

Entities

People

  • T. S. Blyth
  • W. C. Hardy

Organizations

  • Center for Naval Analyses

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  • Biomedical
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  • Mathematics

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