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Congruence lattices of semilattices

Freese, Ralph and Nation, J. B. (1973) Congruence lattices of semilattices. Pacific Journal of Mathematics, 49 (1). pp. 51-58. ISSN 0030-8730.

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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.

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Additional Information:© 1973 Pacific Journal of Mathematics. Received July 10, 1972.
Issue or Number:1
Record Number:CaltechAUTHORS:FREpjm73
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:843
Deposited By: Tony Diaz
Deposited On:19 Oct 2005
Last Modified:02 Oct 2019 22:37

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