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Principal tolerances on lattices. (English) Zbl 0844.08004

Summary: The author presents conditions under which every finitely generated congruence is principal and conditions under which principal congruences or tolerances form a lattice.

MSC:

08A30 Subalgebras, congruence relations
06D99 Distributive lattices
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References:

[1] Baker K. A.: Primitive satisfaction and equational problems for lattices and other algebras. Trans. Amer. Math. Soc., 190 (1974), 125-150. · Zbl 0291.08001 · doi:10.2307/1996955
[2] Chajda I.: A Mal’cev condition for congruence principal permutable varieties. Algebra Univ., 19 (1984), 337-340. · Zbl 0552.08006 · doi:10.1007/BF01201102
[3] Chajda I.: Algebras with principal tolerances. Math. Slovaca, 37 (1987), 169-172. · Zbl 0617.08012
[4] Chajda I., Zelinka B.: Minimal compatible tolerances on lattices. Czech. Math. J., 27 (1977), 452-459. · Zbl 0379.06002
[5] Duda J.: Polynomial pairs characterizing principality. Collog. Math. Soc. J. Bolyai 43., Lectures in universal algebra, Szeged 1983, North-Holland 1985, 109-122. · Zbl 0595.08005
[6] Quackenbush R. W.: Varieties with n-principal compact congruences. Algebra Univ., 14 (1982), 292-296. · Zbl 0493.08006 · doi:10.1007/BF02483933
[7] ZlatoŇ° P.: A Mal’cev condition for compact congruences to be principal. Acta Sci. Math. (Szeged), 43 (1981), 383-387. · Zbl 0478.08010
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