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Finite semigroups whose varieties have uncountably many subvarieties
Citation
Jackson, MG, Finite semigroups whose varieties have uncountably many subvarieties, Journal of Algebra, 228, (2) pp. 512-535. ISSN 0021-8693 (2000) [Refereed Article]
DOI: doi:10.1006/jabr.1999.8280
Abstract
For several large classes of semigroups we provide a description of all semigroups which generate varieties with uncountably many subvarieties. These include the class of all Rees quotients of free monoids, the class of finite orthodox monoids, the class of monoids of index greater than two, and the class of finite inherently not finitely based semigroups. The first example of a finite, finitely based semigroup generating a variety with uncountably many subvarieties is presented and a number of related results are obtained. All varieties found with uncountably many subvarieties contain uncountable chains of subvarieties with the same ordering as the real numbers. © 2000 Academic Press.
Item Details
Item Type: | Refereed Article |
---|---|
Research Division: | Mathematical Sciences |
Research Group: | Pure Mathematics |
Research Field: | Group Theory and Generalisations |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding Knowledge |
Objective Field: | Expanding Knowledge in the Mathematical Sciences |
Author: | Jackson, MG (Dr Marcel Jackson) |
ID Code: | 18702 |
Year Published: | 2000 |
Web of Science® Times Cited: | 29 |
Deposited By: | Mathematics |
Deposited On: | 2000-08-01 |
Last Modified: | 2011-08-04 |
Downloads: | 0 |
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