J Austral Math Soc Ser A 51 pp381--399, 1991.

Totally Commutative Semigroups

Józef Dudek and Andrzej Kisielewicz

(Received 4 April 1989; revised 23 February 1990)

Abstract

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.

1991 AMS Subject Classification: 20M07, 20M05, 08B15; secondary 20M14, 08B05

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Authors

Józef Dudek: Institute of Mathematics, Wroclaw University, P1. Grunwaldzki 2/4, 50-384 Wroclaw, Poland.
Andrzej Kisielewicz: Institute of Mathematics, Technical University of Wroclaw, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland.

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