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On equational theories of semilattices with operators

Published online by Cambridge University Press:  17 April 2009

J. Ježek ,
P. PudláK  and
J. Tůma
J. Ježek
Affiliation:
Department of Algebra, Faculty of Mathematics and Physics, Sokolovská 83, 180 00 Prague 8, Czechoslovakia
P. PudláK
Affiliation:
Department of Algebra, Faculty of Mathematics and Physics, Sokolovská 83, 180 00 Prague 8, Czechoslovakia
J. Tůma
Affiliation:
Mathematical Institute, Žitná, 25 115 67 Prague 1, Czechoslovakia
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Abstract

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In 1986, Lampe presented a counterexample to the conjecture that every algebraic lattice with a compact greatest element is isomorphic to the lattice of extensions of an equational theory. In this paper we investigate equational theories of semi-lattices with operators. We construct a class of lattices containing all infinitely distributive algebraic lattices with a compact greatest element and closed under the operation of taking the parallel join, such that every element of the class is isomorphic to the lattice of equational theories, extending the theory of a semilattice with operators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 57 - 70
Copyright
Copyright © Australian Mathematical Society 1990

References

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