Quasi-Residuated Mappings and Baer Assemblies.
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA
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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
- Theoretical Mathematics