2-uniform congruences in majority algebras and a closure operator (Q995379)

A congruence \(\alpha \) of a finite algebra is called uniform if all its classes have the same number of elements (if all the \(\alpha\)-classes are two-element then \(\alpha \) is said to be a \(2\)-uniform congruence). If all congruences of \(A\) are uniform then \(A\) is said to be a uniform algebra. In [Acta Sci. Math. 71, No. 3--4, 457--460 (2005; Zbl 1101.06004)], \textit{K. Kaarli} proved that uniform finite lattices are congruence permutable. The main result of the present paper is in connection with the result of Kaarli: For every finite algebra \(A\) with a majority term any two \(2\)-uniform congruences of \(A\) permute.