Let V be a variety with two distinct nullary operations 0 and 1. An algebra 𝔄 ∈ V is called balanced if for each Φ,Ψ ∈ Con(𝔄), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every 𝔄 ∈ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1031,
author = {Ivan Chajda and G\"unther Eigenthaler},
title = {Balanced congruences},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {21},
year = {2001},
pages = {105-114},
zbl = {1065.08004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1031}
}
Ivan Chajda; Günther Eigenthaler. Balanced congruences. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 105-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1031/
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