×

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)

MSC:

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

References:

[1] Grätzer G.: General Lattice Theory. Berlin, 1978. · Zbl 0436.06001
[2] Maľcev A.I.: On the general theory of algebraic systems. (Russian), Matem.Sbornik 35 (1954), 3-20.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.