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Distributivity and modularity of lattices of tolerance relations. (English) Zbl 0469.08003


MSC:

08B10 Congruence modularity, congruence distributivity
08B05 Equational logic, Mal’tsev conditions
08A30 Subalgebras, congruence relations
08A40 Operations and polynomials in algebraic structures, primal algebras
08A60 Unary algebras
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References:

[1] A. Day,A characterization of modularity for congruence lattices of algebras, Canad. Math. Bull.12 (1969), 167–173. · Zbl 0181.02302
[2] B. Jónsson,Algebras whose congruence lattices are distributive, Math. Scand21 (1967), 110–121. · Zbl 0167.28401
[3] I. Chajda,Lattices of compatible relations, Archiv. Math. (Brno)13 (1977), 89–96. · Zbl 0372.08002
[4] I. Chajda, B. Zelinka,Lattices of tolerances, Časop. pěst. matem.102 (1977), 10–24. · Zbl 0354.08011
[5] I. Chajda, B. Zelinka,Minimal compatible tolerances on lattices, Czech. Math. J.27 (1977), 452–459. · Zbl 0379.06002
[6] I. Chajda,A characterization of distributive lattices by tolerance lattices, Arch. Math. (Brno),15 (1979), 203–204. · Zbl 0439.06008
[7] I. Chajda,Regularity and permutability of congruences, Algebra Univ.,11 (1980), 159–162. · Zbl 0449.08007
[8] D. Schweigert,On order-polynomially complete algebras, Notices of AMS, vol. 25 (1978), No. 6. · Zbl 0384.06011
[9] H. Werner,A Mal’cev condition on admissible relations, Algebra Univ.3 (1973), 263. · Zbl 0276.08004
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