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Varieties having directly decomposable congruence classes. (English) Zbl 0606.08001
The paper contains a Mal’cev type condition characterizing varieties whose members have the following property: every congruence class \(C\) on the direct product \(A\times B\) is a Cartesian product \(C=C_ A\times C_ B\). This condition is simplified in the case of \(n\)-permutable varieties. In the modular case, the direct decomposability of congruence classes is equivalent to direct decomposability of congruences.

MSC:
08A30 Subalgebras, congruence relations
08B05 Equational logic, Mal’tsev conditions
08B10 Congruence modularity, congruence distributivity
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