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Complemented uniform lattices

โœ Scribed by Hans Weber

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
160 KB
Volume
105
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

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 uniformity is isomorphic to the product of an arcwise connected complemented lattice and of geometric lattices of finite length each of which endowed with the discrete uniformity. These two results are used to prove a decomposition theorem for modular functions on complemented lattices.

๐Ÿ“œ SIMILAR VOLUMES

Modularly complemented geometric lattice
Modularly complemented geometric lattices
โœ J.Randolph Stonesifer ๐Ÿ“‚ Article ๐Ÿ“… 1980 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 318 KB

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.