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Every finite chain is the tolerance lattice of some lattice. (English) Zbl 0587.06001
LT(A) denotes the lattice of all tolerances \((=\) reflexive, symmetric, and compatible binary relations) on an algebra A. Theorem. For each finite chain C there exists a finite lattice L such that \(C\cong LT(L)\).
Reviewer: J.Duda

MSC:
06B05 Structure theory of lattices
06B10 Lattice ideals, congruence relations
06B15 Representation theory of lattices
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