A new method in the finite basis problem with applications to rank 2 transformation semigroups

G. Mashevitzky

doi:10.1142/S0218196707004232

A new method in the finite basis problem with applications to rank 2 transformation semigroups

G. Mashevitzky

Department of Mathematics

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

2 Scopus citations

Abstract

We prove that the semigroup of all transformations of a 3-element set with rank at most 2 does not have a finite basis of identities. This gives a negative answer to a question of Shevrin and Volkov. It is worthwhile to notice that the semigroup of transformations with rank at most 2 of an ra-element set, where n > 4, has a finite basis of identities. A new method of constructing finite non-finitely based semigroups is developed.

Original language	English
Pages (from-to)	1431-1463
Number of pages	33
Journal	International Journal of Algebra and Computation
Volume	17
Issue number	7
DOIs	https://doi.org/10.1142/S0218196707004232
State	Published - 1 Nov 2007

Keywords

Circulant graph
Completely 0-simple semigroup
Identity
The finite basis problem
Transformation semigroup

ASJC Scopus subject areas

General Mathematics

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10.1142/S0218196707004232

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KW - Completely 0-simple semigroup

KW - Identity

KW - The finite basis problem

KW - Transformation semigroup

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A new method in the finite basis problem with applications to rank 2 transformation semigroups

Abstract

Keywords

ASJC Scopus subject areas

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