Varieties which are locally regular and permutable at 0. (English) Zbl 1038.08005

Summary: A variety \({\mathcal V}\) is locally regular if for each algebra \({\mathcal A}\) of \({\mathcal V}\) and every \(\theta\in \text{Con\,}{\mathcal A}\), the \(0\)-class is determined by every class of \(\theta\). \({\mathcal V}\) is permutable at \(0\) if for every \(\theta\), \(\phi\in \text{Con\,}{\mathcal A}\) the \(0\)-class of \(\theta\cdot\phi\) equals the \(0\)-class of \(\phi\cdot\theta\). Varieties having both of these conditions are characterized by a Mal’tsev-type condition.


08B05 Equational logic, Mal’tsev conditions
08A30 Subalgebras, congruence relations
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