Article
The Smallest Monoid that Generates a Non-Cross Variety
Journal of Xiamen University (Natural Science)
Document Type
Article
Publication Date
1-1-2014
Keywords
- Monoid,
- Variety,
- Cross Variety
Disciplines
Abstract
A monoid variety is a class of monoids that is closed under the formation of homomorphic images, submonoids, and arbitrary direct products. A finitely generated, finitely based variety of monoids that contains only finitely many subvarieties is a Cross monoid variety. The 5-element monoid M5 is first shown to generate a non-Cross monoid variety. Then it is shown that, up to isomorphism and anti-isomorphism, any monoid of order five or less different from M5 generates a Cross monoid variety. Therefore up to isomorphism and anti-isomorphism, M5 is the only smallest monoid that generates a non-Cross monoid variety.
ORCID ID
0000-0002-1662-3734
ResearcherID
I-6970-2013
DOI
10.6043/j.issn.0438-0479.2014.01.001
Citation Information
Edmond W. H. Lee and Wen Ting Zhang. "The Smallest Monoid that Generates a Non-Cross Variety" Journal of Xiamen University (Natural Science) Vol. 53 Iss. 1 (2014) p. 1 - 4 ISSN: 0438-0479 Available at: http://works.bepress.com/edmond-lee/27/