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Matchings for linearly indecomposable modular lattices

โœ Scribed by Klaus Reuter

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
181 KB
Volume
63
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Given a finite lattice L, let J(L) (M(L)) denote the set of nonzero join irreducible (nonunit meet irreducible) elements of L. A finite lattice L is said to be linearly indecomposable if there do not exist x, y E L with x < y such that z cx or z 2 y for all z E L{x, y}. We prove: Every finite linearly indecomposable modular lattice L has a matching of J(L) to M(L), i.e., a bijection f of J(L) to M(L) with x <f(x) for each x E J(L).

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