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Article Dans Une Revue International Journal of Algebra and Computation Année : 2003

Sublattices of lattices of order-convex sets, II. Posets of finite length

Marina V. Semenova
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Résumé

For a positive integer n, we denote by SUB (resp., SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (resp., P of length at most n). We prove the following results: (1) SUBn is a finitely based variety, for any n ? 1. (2) SUB2 is locally finite. (3) A finite atomistic lattice L without D-cycles belongs to SUB iff it belongs to SUB2; this result does not extend to the nonatomistic case. (4) SUBn is not locally finite for n ? 3.
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Dates et versions

hal-00003979 , version 1 (21-01-2005)

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Marina V. Semenova, Friedrich Wehrung. Sublattices of lattices of order-convex sets, II. Posets of finite length. International Journal of Algebra and Computation, 2003, 13 (5), pp.543--564. ⟨10.1142/S0218196703001547⟩. ⟨hal-00003979⟩
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