Finitely based finite involution semigroups with non-finitely based reducts

Edmond W. H. Lee

doi:10.2989/16073606.2015.1068239

Finitely based finite involution semigroups with non-finitely based reducts

Edmond W. H. Lee

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

Abstract

Since the study of the finite basis problem for finite semigroups began in the 1960s, it has been unknown if there exists any finite involution semigroup that is finitely based but the reduct of which is non-finitely based. The present article exhibits an example of such an involution semigroup of order n + 5 for any positive integer n.

Original language	American English
Pages (from-to)	217–243
Number of pages	27
Journal	Quaestiones Mathematicae
Volume	39
Issue number	2
DOIs	https://doi.org/10.2989/16073606.2015.1068239
State	Published - Apr 2016

Bibliographical note

Publisher Copyright:
© 2016 NISC (Pty) Ltd.

ASJC Scopus Subject Areas

Mathematics (miscellaneous)

Keywords

Semigroup
Involution semigroup
Identity
Basis
Irredundant basis
Finite basis
involution semigroup
identity
irredundant basis#finite basis
basis

Disciplines

Mathematics

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10.2989/16073606.2015.1068239

Cite this

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abstract = " Since the study of the finite basis problem for finite semigroups began in the 1960s, it has been unknown if there exists any finite involution semigroup that is finitely based but the reduct of which is non-finitely based. The present article exhibits an example of such an involution semigroup of order n + 5 for any positive integer n.",

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AU - Lee, Edmond W. H.

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AB - Since the study of the finite basis problem for finite semigroups began in the 1960s, it has been unknown if there exists any finite involution semigroup that is finitely based but the reduct of which is non-finitely based. The present article exhibits an example of such an involution semigroup of order n + 5 for any positive integer n.

KW - Semigroup

KW - Involution semigroup

KW - Identity

KW - Basis

KW - Irredundant basis

KW - Finite basis

KW - involution semigroup

KW - identity

KW - irredundant basis#finite basis

KW - basis

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DO - 10.2989/16073606.2015.1068239

M3 - Article

SN - 1607-3606

VL - 39

SP - 217

EP - 243

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

IS - 2

ER -

Finitely based finite involution semigroups with non-finitely based reducts

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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