Geodesic
Balanced congruences
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 105-114.

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Let V be a variety with two distinct nullary operations 0 and 1. An algebra ∈ V is called balanced if for each Φ,Ψ ∈ Con(), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every ∈ V is balanced. In this paper, balanced varieties are characterized by a Mal'cev condition (Theorem 3). Furthermore, some special results are given for varieties of bounded lattices.
Keywords: balanced congruence, balanced algebra, balanced variety, Mal'cev condition 
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Chajda, Ivan; Eigenthaler, Günther. Balanced congruences. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 105-114. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a9/

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[4] A.I. Mal'cev, On the general theory of algebraic systems (Russian), Mat. Sb. 35 (1954), 3-20.