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Locality of DS and associated varieties


Jones, PR and Trotter, PG, Locality of DS and associated varieties, Journal of Pure and Applied Algebra, 104, (3) pp. 275-301. ISSN 0022-4049 (1995) [Refereed Article]

DOI: doi:10.1016/0022-4049(94)00054-X


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. © 1995 Elsevier Science B.V. All rights reserved.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Trotter, PG (Dr Peter Trotter)
ID Code:4780
Year Published:1995
Web of Science® Times Cited:21
Deposited By:Mathematics
Deposited On:1995-08-01
Last Modified:2011-08-24

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