Niederle, Josef Conditions for transitive principal tolerances. (English) Zbl 0686.08003 Czech. Math. J. 39(114), No. 2, 380-381 (1989). 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 Cited in 2 Documents MSC: 08A30 Subalgebras, congruence relations 08B05 Equational logic, Mal’tsev conditions Keywords:transitive principal tolerances; term condition Citations:Zbl 0603.08003 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Niederle J.: Conditions for trivial principal tolerances. Arch. Math. (Brno) 19 (1983), 145-152. · Zbl 0538.08002 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.