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Zbl 0606.08001
Duda, Jaromír
Varieties having directly decomposable congruence classes. (English)
[J] Čas. Pěstování Mat. 111, 394-403 (1986). ISSN 0528-2195

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 $C=C\sb A\times C\sb B$. 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.
[I.Chajda]

MSC 2000:: *08A30 Subalgebras of general algebraic systems
08B05 Equational logic in varieties of algebras
08B10 Congruence modularity and generalizations in varieties of algebras

Keywords: Mal'cev type condition; direct product; Cartesian product; n-permutable varieties; direct decomposability of congruence classes; direct decomposability of congruences

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