Tolerances and congruences on lattices
نویسندگان
چکیده
منابع مشابه
Notes on Planar Semimodular Lattices. Ii. Congruences
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We call a lattice L isoform, if for any congruence relation Θ of L, all congruence classes of Θ are isomorphic sublattices. We prove that for every finite distributive lattice D, there exists a finite isoform lattice L such that the congruence lattice of L is isomorphic to D.
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In [L4] we showed that, under certain conditions, a variety satisfies a given congruence identity if and only if it satisfies the same tolerance identity. Moreover, we mentioned that a parallel result holds for Mal’cev conditions arising from graphs. In the present note we give detailed definitions and state these more general results. The motivating example for our constructions is the followi...
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A variety V has tolerances permutable with factor congruences if for any A1, A2 of V and every tolerance T on A1 × A2 we have T ◦ Π1 = Π1 ◦ T and T ◦ Π2 = Π2 ◦ T , where Π1,Π2 are factor congruences. If B is a subalgebra of A1×A2, the congruences Θi = Πi∩B are called decomposing congruences. V has tolerances permutable with decomposing congruences if T ◦ Θi = Θi ◦ T (i = 1, 2) for each A1, A2 ∈...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1986
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1986.102071