A Characterization of a Semimodular Lattice

Studia Logica 106 (4):691-698 (2018)

Authors
Abstract
A geometric lattice is the lattice of closed subsets of a closure operator on a set which is zero-closure, algebraic, atomistic and which has the so-called exchange property. There are many profound results about this type of lattices, the most recent one of which, due to Czédli and Schimdt, says that a lattice L of finite length is semimodular if and only if L has a cover-preserving embedding into a geometric lattice G of the same length. The goal of our paper is to offer the following result: a lattice of finite length is semimodular if and only if every cell in L is a 4-element Boolean lattice and the 7-element non-distributive atomistic lattice having 3 atoms is not a cover-preserving sublattice of L.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11225-017-9761-9
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,940
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Some Remarks on the Algebraic Structure of the Medvedev Lattice.Andrea Sorbi - 1990 - Journal of Symbolic Logic 55 (2):831-853.
On the Structure of the Medvedev Lattice.Sebastiaan A. Terwijn - 2008 - Journal of Symbolic Logic 73 (2):543 - 558.
Infinite Substructure Lattices of Models of Peano Arithmetic.James H. Schmerl - 2010 - Journal of Symbolic Logic 75 (4):1366-1382.
Lattice Representations for Computability Theory.Peter A. Fejer - 1998 - Annals of Pure and Applied Logic 94 (1-3):53-74.
Priestley Duality for Some Subalgebra Lattices.Georges Hansoul - 1996 - Studia Logica 56 (1-2):133 - 149.
Nondiversity in Substructures.James H. Schmerl - 2008 - Journal of Symbolic Logic 73 (1):193-211.

Analytics

Added to PP index
2017-10-03

Total views
33 ( #238,225 of 2,235,511 )

Recent downloads (6 months)
3 ( #573,407 of 2,235,511 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature