On the one principal congruence identity. (English) Zbl 0663.08003

Chajda, Ivan

Arch. Math., Brno 23, 187-190 (1987).

The author investigates conditions when in a variety with a nullary operation 0: \(\theta\) (x,0)\(\subseteq \theta (x,0)\cdot \theta (y,0)\) holds. For this aim he investigates properties of tolerances (reflexive, symmetric subalgebras of \(A\times A)\). The main theorem is a Mal’tsev condition for principal tolerances, by which some corollaries follow for the above property.

Reviewer: G.Matthiessen

MSC:

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

Keywords:

principal congruence; Mal’tsev condition; principal tolerances