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

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

2005-01-21

arxiv.org/abs/math/0501340v1

International Journal of Algebra and Computation 13, no. 5 (2003) 543-564

Mathematics

General Mathematics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Sublattices of lattices of order-convex sets, II. Posets of finite length does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sublattices of lattices of order-convex sets, II. Posets of finite length, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sublattices of lattices of order-convex sets, II. Posets of finite length will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-593861