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The finite basis problem for pseudovariety

Published online by Cambridge University Press:  14 November 2011

V. B. Repnitskiǐ  and
M. V. Volkov
V. B. Repnitskiǐ
Affiliation:
Department of Mathematics and Mechanics, Ural State University, 620083 Ekaterinburg, Russia
M. V. Volkov
Affiliation:
Department of Mathematics and Mechanics, Ural State University, 620083 Ekaterinburg, Russia
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Abstract

We show that the pseudovariety generated by all semigroups of order-preserving transformations of a finitechain has no finite pseudoidentity basis.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 3 , 1998 , pp. 661 - 669
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

1Almeida, J.. Finite Semigroups and Universal Algebra (Singapore: World Scientific, 1995).Google Scholar
2Almeida, J. and Volkov, M. V.. The gap between partial and full. Internat. J. Algebra Comput. (to appear).Google Scholar
3Anderson, M. and Edwards, C. C.. A representation theorem for distributive l-monoids. Canad. Math. Bull. 27 (1984), 238–40.Google Scholar
4Choudhuri, A. C.. The doubly distributive m-lattice. Bull. Calcutta Math. Soc. 49 (1957), 71–4.Google Scholar
5Cowan, D. F. and Reilly, N. R.. Partial cross-sections of symmetric invese semigroups. Internat. J. Algebra Comput. 5 (1995), 259–87.Google Scholar
6Edwards, C. C. and Anderson, M.. Lattice properties of the symmetric weakly inverse semigroup on a totally ordered set. J. Austral. Math. Soc. 31 (1981), 395–404.CrossRefGoogle Scholar
7Fernandes, V. H.. Semigroups of order-preserving mappings on a finite chain: a new class of divisors. Semigroup Forum 54 (1997), 230–6.CrossRefGoogle Scholar
8Higgins, P. M.. Pseudovarieties generated by transformation semigroups. In Semigroups and Their Applications Including Semigroup Rings, eds Ponizovskii, J. S. and Kublanovsky, S. (Berlin: Walter de Gruyter) (to appear).Google Scholar
9Reiterman, J.. The Birkhoff theorem for finite algebras. Algebra Universalis 14 (1982), 1–10.CrossRefGoogle Scholar