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Locality of DS and associated varieties
journal contributionposted on 2023-05-16, 09:46 authored by Jones, PR, Trotter, PG
We prove that the pseudovariety DS, of all finite monoids, each of whose regular D-classes is a subsemigroup, is local. (A pseudovariety (or variety) V is local if any category whose local monoids belong to V divides a member of V.) The proof uses the "kernel theorem" of the first author and Pustejovsky together with the description by Weil of DS as an iterated "block product". The one-sided analogues of these methods provide wide new classes of local pseudovarieties of completely regular monoids. We conclude, however, with the second author's example of a variety (and a pseudovariety) of completely regular monoids that is not local. Â© 1995 Elsevier Science B.V. All rights reserved.
Publication titleJournal of Pure and Applied Algebra
Department/SchoolSchool of Natural Sciences
PublisherElsevier Science Bv
Place of publicationPo Box 211, Amsterdam, Netherlands, 1000 Ae