Permutability of congruences in varieties with idempotent operations. (English) Zbl 0768.08006

Author’s summary: It is proven that if a variety \(V\) with at least two binary idempotent operations \(f\), \(g\) is permutable, then there exists a ternary term \(t(x,y,z)\) such that \(t(x,x,z)=f(x,z)\) and \(t(x,z,z)=g(x,z)\). If, moreover, reducts of algebras of \(V\) are lattices, this condition is necessary and sufficient for the permutability of \(V\).
Reviewer: R.A.Alo (Houston)


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


[1] Grätzer G.: General Lattice Theory. Berlin, 1978. · Zbl 0436.06001
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