Every at most four element algebra has a Mal’cev theory for permutability. (English) Zbl 0779.08001

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 \(A\).


08A30 Subalgebras, congruence relations
08B05 Equational logic, Mal’tsev conditions
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