A note on some local properties of weak congruences (Q2759854)

A weak congruence relation is a symmetric and transitive subalgebra of \(A\times A\). An algebra \(A\) with a constant \(0\) is weak congruence modular at \(0\) whenever \([0]\alpha\vee (\beta\wedge\gamma)= [0](\alpha\vee \beta)\wedge\gamma\) holds for any weak congruences \(\alpha\), \(\beta\), \(\gamma\), \(\alpha\subseteq\gamma\). It is shown that algebras that are weak congruence modular \(0\) are subalgebra modular and have the CEP at \(0\). Conversely some sufficient conditions for modularity of weak congruences at \(0\) are given.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].