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On the Structure of Finitely Presented Lattices
Published online by Cambridge University Press: 20 November 2018
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A lattice L is finitely presented (or presentable) if and only if it can be described with finitely many generators and finitely many relations. Equivalently, L is the lattice freely generated by a finite partial lattice A, in notation, L = F(A). (For more detail, see Section 1.5 of [6].)
It is an old “conjecture” of lattice theory that in a finitely presented (or presentable) lattice the elements behave “freely” once we get far enough from the generators.
In this paper we prove a structure theorem that could be said to verify this conjecture.
THEOREM 1. Let L be a finitely presentable lattice. Then there exists a congruence relation θ such that L/θ is finite and each congruence class is embeddable in a free lattice.
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- Copyright © Canadian Mathematical Society 1981
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