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Modularly complemented geometric lattices

โœ Scribed by J.Randolph Stonesifer

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
318 KB
Volume
32
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

A geometric lattice L is strongly uniform if the quotients [x,, l] and [x,, l] are isomorphic for all x,, _QE L of the same rank. It is shown that if L is a simple geometric lattiue in which each element has a modular complement then L is strongly uniform.

๐Ÿ“œ SIMILAR VOLUMES

Complemented uniform lattices
Complemented uniform lattices
โœ Hans Weber ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 160 KB

It is proved that the completion of a complemented modular lattice with respect to a Hausdorff lattice uniformity which is metrizable or exhaustive is a complemented modular lattice. It is then shown that a complete complemented modular lattice endowed with a Hausdorff order continuous lattice unifo