Slim Semimodular Lattices. II. A Description by Patchwork Systems

被引：0
作者：
Gábor Czédli
E. Tamás Schmidt
机构：
[1] University of Szeged,Bolyai Institute
[2] Mathematical Institute of the Budapest University of Technology and Economics,undefined
来源：
Order | 2013年 / 30卷
关键词：
Slim lattice; Semimodularity; Planar lattice; Patchwork; Primary 06C10;
D O I：
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学科分类号：
摘要：
Rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in Acta Sci Math 75:29–48, 2009. A patch lattice is a rectangular lattice whose weak corners are coatoms. As a variant of gluing, we introduce the concept of a patchwork system. We prove that every glued sum indecomposable, planar, semimodular lattice is a patchwork of its maximal patch lattice intervals. For a planar modular lattice, our patchwork system is the same as the S-glued system introduced by C. Herrmann in Math Z 130:255–274, 1973. Among planar semimodular lattices, patch lattices are characterized as the patchwork-irreducible ones. They are also characterized as the indecomposable ones with respect to gluing over chains; this gives another structure theorem.
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页码：689 / 721
页数：32
相关论文
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