Conditions for factorable relations. (English) Zbl 0795.08007

It is shown that a variety \(\mathcal V\) has the Fraser-Horn property for congruences (tolerances) iff the congruence (tolerance) condition \(\langle\langle x,x,x\rangle,\langle y,y,x\rangle\rangle\in \Theta\) implies \(\langle\langle x,x,y\rangle,\langle y,x,y\rangle\rangle\in \Theta\) \((\langle\langle x,x,x\rangle,\langle y,y,x\rangle\rangle,\langle\langle y,y,y\rangle,\langle y,y,x\rangle\rangle\in T\) imply \(\langle\langle x,y,y\rangle,\langle y,y,x\rangle\rangle\in T)\) holds for any congruence \(\Theta\) (tolerance \(T\)) on \(A\times A\times A\), \(x,y\in A\in{\mathcal V}\). The former conditions were written in three (four, respectively) variables.
Reviewer: J.Duda (Brno)


08B05 Equational logic, Mal’tsev conditions
Full Text: EuDML


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