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**Conditions for transitive principal tolerances.**
*(English)*
Zbl 0686.08003

An algebra A has transitive principal tolerances (i.e. it is principal tolerance trivial in other terminology) if for each \(a,b\in A\), the principal tolerance T(a,b) is a congruence on A, i.e. \(T(a,b)=\theta (a,b)\). A variety \({\mathcal V}\) has transitive principal tolerances if each \(A\in {\mathcal V}\) has this property. The first characterization of such varieties by a \(\forall \exists\)-term condition was given by the reviewer [Ann. Univ. Sci. Budap., Rolando Eötvös, Sect. Math. 28, 37-47 (1985; Zbl 0603.08003)]. This paper contains other types of \(\forall \exists\)- term conditions characterizing such varieties.

Reviewer: I.Chajda

### Citations:

Zbl 0603.08003### References:

[1] | Niederle J.: Conditions for trivial principal tolerances. Arch. Math. (Brno) 19 (1983), 145-152. · Zbl 0538.08002 |

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