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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A ternary function for distributivity and permutability of an equivalence lattice


Author: Ivan Korec
Journal: Proc. Amer. Math. Soc. 69 (1978), 8-10
MSC: Primary 08A25; Secondary 06A35
MathSciNet review: 0472648
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Abstract: The main result of the paper is

Theorem 1. Let A be a countable set and L be a complete sublattice of the equivalence lattice on A. The following are equivalent

(i) L is a distributive lattice of permutable equivalence relations.

(ii) There is an algebra with congruence lattice L among the fundamental operations of which is a ternary function f with the property

$\displaystyle \quad f(a,b,b) = f(a,b,a) = f(b,b,a) = a$ ($ 1$)

for all $ a, b \in A$.

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DOI: https://doi.org/10.1090/S0002-9939-1978-0472648-8
Article copyright: © Copyright 1978 American Mathematical Society