Small semigroups generating varieties with continuum many subvarieties

Charles C. Edmunds; Edmond W. H. Lee; Ken W.K. Lee

doi:10.1007/s11083-010-9142-8

Small semigroups generating varieties with continuum many subvarieties

Charles C. Edmunds
, Edmond W. H. Lee
, Ken W.K. Lee

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.

Original language	American English
Pages (from-to)	83–100
Journal	Order
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s11083-010-9142-8
State	Published - Mar 1 2010
Externally published	Yes

Keywords

Semigroup
Monoid
Variety
Finitely based
Hereditarily finitely based

Disciplines

Mathematics

Access to Document

10.1007/s11083-010-9142-8License: Unspecified

Cite this

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abstract = " The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.",

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AU - Lee, Edmond W. H.

AU - Lee, Ken W.K.

PY - 2010/3/1

Y1 - 2010/3/1

N2 - The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.

AB - The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.

KW - Semigroup

KW - Monoid

KW - Variety

KW - Finitely based

KW - Hereditarily finitely based

UR - http://www.webofscience.com/wos/woscc/full-record/WOS:000274657300007

UR - https://www.scopus.com/pages/publications/84864880744

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VL - 27

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EP - 100

JO - Order

JF - Order

IS - 1

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Small semigroups generating varieties with continuum many subvarieties

Abstract

Keywords

Disciplines

Access to Document

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