## 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.

### MSC:

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

### References:

 [1] Chajda I.: Regularity and permutability of congruences. Algebra Universalis 11 (1980), 159-162. · Zbl 0449.08007 [2] Chajda I.: Locally regular varieties. Acta Sci. Math. (Szeged), 64 (1998), 431-435. · Zbl 0913.08006 [3] Csákány B.: Characterization of regular varieties. Acta Sci. Math. (Szeged), 31 (1970), 187-189. · Zbl 0216.03302 [4] Fichtner K.: Eine Bemerkung über Mannigfaltigkeiten Universeller Algebren mit Idealen. Monats. d. Deutsch. Akad. d. Wiss. (Berlin), 12 (1970), 21-25. · Zbl 0198.33601 [5] Gumm H.-P., Ursini A.: Ideals in universal algebras. Algebra Universalis 19 (1984), 45-54. · Zbl 0547.08001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.