Varieties having directly decomposable congruence classes. (English) Zbl 0606.08001

Duda, Jaromír

Čas. Pěstování Mat. 111, 394-403 (1986).

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.

Reviewer: Ivan Chajda (Olomouc)

MSC:

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

Keywords:

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