Slim Semimodular Lattices. I. A Visual Approach

被引：30

作者：

Czedli, Gabor ^{[1
]}

Schmidt, E. Tamas ^{[2
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

[2] Budapest Univ Technol & Econ, Math Inst, H-1521 Budapest, Hungary

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2012年 / 29卷 / 03期

关键词：

Semimodular lattice; Slim lattice; Planar lattice; Join-homomorphism; Contour; Fork; Corner;

D O I：

10.1007/s11083-011-9215-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A finite lattice L is called slim if no three join-irreducible elements of L form an antichain. Slim lattices are planar. After exploring some elementary properties of slim lattices and slim semimodular lattices, we give two visual structure theorems for slim semimodular lattices.

引用

页码：481 / 497

页数：17

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