On the Structure of Finitely Presented Lattices
1981 ◽
Vol 33
(2)
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pp. 404-411
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Keyword(s):
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.
1992 ◽
Vol 44
(2)
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pp. 252-269
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Keyword(s):
2019 ◽
Vol 4
(1)
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pp. 151-162
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1979 ◽
Vol 31
(1)
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pp. 69-78
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1970 ◽
Vol 22
(3)
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pp. 472-475
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Keyword(s):
1978 ◽
2013 ◽
Vol 59
(1)
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pp. 209-218
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