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Published 1973 | public
Journal Article Open

Congruence lattices of semilattices

Abstract

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if V is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then all the members of V are groups with exponent dividing a fixed finite number.

Additional Information

© 1973 Pacific Journal of Mathematics. Received July 10, 1972.

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August 22, 2023
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October 13, 2023