Locality of DS and associated varieties
Document Type
Article
Language
eng
Publication Date
11-10-1995
Publisher
Elsevier
Source Publication
Journal of Pure and Applied Algebra
Source ISSN
0022-4049
Abstract
We prove that the pseudovariety DS, of all finite monoids, each of whose regular D" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.4px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">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.
Recommended Citation
Jones, Peter R. and Trotter, Peter G., "Locality of DS and associated varieties" (1995). Mathematics, Statistics and Computer Science Faculty Research and Publications. 606.
https://epublications.marquette.edu/mscs_fac/606
Comments
Journal of Pure and Applied Algebra, Vol 104, No. 3 (November 10, 1995): 275-301. DOI.