## 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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