Chajda, Ivan Every at most four element algebra has a Mal’cev theory for permutability. (English) Zbl 0779.08001 Math. Slovaca 41, No. 1, 35-39 (1991). For any algebra \(A\) with at most four elements, it is proved that \(A\) has permutable congruences if and only if there exists a ternary Mal’tsev function on \(A\) which is compatible with all congruences of \(A\). Reviewer: J.Ježek (Columbia) Cited in 2 Documents MSC: 08A30 Subalgebras, congruence relations 08B05 Equational logic, Mal’tsev conditions Keywords:arithmetic variety; permutable congruences; Mal’tsev function PDF BibTeX XML Cite \textit{I. Chajda}, Math. Slovaca 41, No. 1, 35--39 (1991; Zbl 0779.08001) Full Text: EuDML OpenURL References: [1] GUMM H.-P.: Is there a Maľcev theory for single algebras?. Algebra univ., 8, 1978, 320-329. · Zbl 0382.08003 [2] KOREC I.: A ternary function for distributivity and permutability of an equivalence lattice. Proc. Amer. Math. Soc., 69, 1978, 8-10. · Zbl 0382.08004 [3] MAĽCEV A. I.: On the general theory of algebraic systems. Mat. Sborník., 35, 1954, 3-20. [4] PIXLEY A. F.: Distributivity and permutability of congruence relations in equational classes of algebras. Proc. Amer. Math. Soc., 14, 1963, 105-109. · Zbl 0113.24804 [5] PIXLEY A. F.: Local Maľcev conditions. Canad. Math. Bull., 15, 1972, 559-568. · Zbl 0254.08009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.