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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
##### Keywords:
lattice of all tolerances; finite chain; finite lattice