Abstract
SynopsisWe 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.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences
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