A ternary function for distributivity and permutability of an equivalence lattice
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- by Ivan Korec
- Proc. Amer. Math. Soc. 69 (1978), 8-10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0472648-8
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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 \begin{equation}\tag {$1$} \quad f(a,b,b) = f(a,b,a) = f(b,b,a) = a\end{equation} for all $a, b \in A$.References
- George Grätzer, Universal algebra, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0248066
- Bjarni Jónsson, Topics in universal algebra, Lecture Notes in Mathematics, Vol. 250, Springer-Verlag, Berlin-New York, 1972. MR 0345895
- A. F. Pixley, Completeness in arithmetical algebras, Algebra Universalis 2 (1972), 179–196. MR 321843, DOI 10.1007/BF02945027
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 8-10
- MSC: Primary 08A25; Secondary 06A35
- DOI: https://doi.org/10.1090/S0002-9939-1978-0472648-8
- MathSciNet review: 0472648