A NEW LOOK AT THE SEMIMODULAR LATTICES A GEOMETRIC APPROACH (NOT FINISHED MANUSCRIPT)
As Schmidt · 2016
This paper is an experiment, how it is possible to treat semimod- ular lattices as geometric shapes. In 2009 I published a paper with Gabor Czedli, (4), we proved that every semimodular lattice L can be obtained from a direct power of a chain G = Cn - geometrically a cube - on an easy way. L is the cover-preserving join-homomorphism of G. We introduce the concept of rectangular semimodular lattices and prove that the building stones of semimodular lattices are special rectangulars, the pigeonholes. The building tool is a special S-verklebte sum (introduced by Christian Herrmann (21)) this is the patchwork. This manuscript includes parts of the papers (2), (3), (4), (5), (6), (7), (8), (9), (10) and (11).