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Tolerance lattice of algebras with restricted similarity type. (English) Zbl 0854.08001

The author shows that for any algebra \(A\) of a finite similarity type there exists an algebra \(B\) of type \((2,1,1)\) such that the lattices of tolerances on \(A\) and \(B\) are isomorphic.
Reviewer: J.Duda (Brno)

MSC:

08A30 Subalgebras, congruence relations
08A62 Finitary algebras
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References:

[1] Chajda I.: Algebraic Theory of Tolerance Relations. Monograph Series of Palacký University, Olomouc, 1991. · Zbl 0747.08001
[2] Chajda I., Czédli G.: A Note on Representation of Lattices by Tolerances. J. of Algebra 148 (1992), 274-275. · Zbl 0777.08002
[3] Grätzer G., Schmidt E. T.: Characterization of congruence lattice of abstract algebras. Acta Sci. Math. (Szeged) 24 (1963), 34-59. · Zbl 0117.26101
[4] Iskander A. A.: The lattice of correspondences of universal algebras. Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 1357-1372
[5] Jónsson B.: Topics in Universal Algebra. Lectures Notes in Math. 250, Springer Verlag, Berlin-Heidelberg-New York, 1972. · Zbl 0225.08001
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