Chajda, Ivan; Czédli, Gábor A note on representation of lattices by tolerances. (English) Zbl 0777.08002 J. Algebra 148, No. 1, 274-275 (1992). A tolerance on an algebra \(A\) is a reflexive and symmetric subalgebra of the Cartesian square of \(A\). Theorem: Let \(L\) be an algebraic lattice. Then there is an algebra \(A\) such that \(L\) is isomorphic to the lattice of all tolerances on \(A\); moreover, every subalgebra of \(A^ 2\) is a tolerance. Reviewer: A.A.Iskander (Lafayette) Cited in 1 Document MSC: 08A30 Subalgebras, congruence relations 06B15 Representation theory of lattices Keywords:lattice of tolerances; algebraic lattice × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Chajda, I., Recent results and trends in tolerances on algebras and varieties, (Finite Algebra and Multiple-valued Logic, Szeged 1979. Finite Algebra and Multiple-valued Logic, Szeged 1979, Colloq. Math. Soc. János Bolyai, Vol. 28 (1981), North-Holland: North-Holland Amsterdam), 69-95 · Zbl 0484.08002 [2] Grätzer, G.; Lampe, W. A., On subalgebra lattices of universal algebras, J. Algebra, 7, 263-270 (1967) · Zbl 0178.01101 [3] Iskander, A. A., The lattice of correspondences of universal algebras, Izv. Akad. Nauk SSSR Ser. Mat., 29, 1357-1372 (1965), [Russian] · Zbl 0207.32501 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.