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Totally commutative semigroups

Part of: Semigroups Varieties

Published online by Cambridge University Press:  09 April 2009

Józef Dudek  and
Andrzej Kisielewicz
Józef Dudek
Affiliation:
Institute of Mathematics Wroclaw UniversityP1. Grunwaldzki 2/4 50-384 Wroclaw, Poland
Andrzej Kisielewicz
Affiliation:
Institute of Mathematics Technical University of WroclawWybrzeze Wyspianskiego 27 50-370 Wroclaw, Poland
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Abstract

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A semigroup is totally commutative if each of its essentially binary polynomials is commutative, or equivalently, if in every polynomial (word) every two essential variables commute. In the present paper we describe all varieties (equational classes) of totally commutative semigroups, lattices of subvarieties for any variety, and their free spectra.

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 20M05: Free semigroups, generators and relations, word problems 08B15: Lattices of varieties 20M14: Commutative semigroups 08B05: Equational logic, Mal′cev (Mal′tsev) conditions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 381 - 399
Copyright
Copyright © Australian Mathematical Society 1991

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