A note on congruence lattices of slim semimodular lattices

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• 作者：Gábor Czédli
• 关键词：06C10 ; rectangular lattice ; planar lattice ; semimodular lattice ; congruence lattice
• 刊名：Algebra Universalis
• 出版年：2014
• 出版时间：November 2014
• 年：2014
• 卷：72
• 期：3
• 页码：225-230
• 全文大小：230 KB
• 参考文献：1. Czédli G.: Representing homomorphisms of distributive lattices as restrictions of congruences of rectangular lattices. Algebra Universalis 67, 313-45 (2012) CrossRef
  2. Czédli, G.: Patch extensions and trajectory colorings of slim rectangular lattices. Algebra Universalis (ALUN-13108)
  3. Czédli G, Schmidt E.T: The Jordan-H?lder theorem with uniqueness for groups and semimodular lattices. Algebra Universalis 66, 69-9 (2011) CrossRef
  4. Czédli G, Schmidt E.T: Slim semimodular lattices. I. A visual approach. Order 29, 481-97 (2012) CrossRef
  5. Czédli, G., Schmidt, E.T.: Slim semimodular lattices. II. A description by patchwork systems. Order, DOI:10.1007/s11083-012-9271-3 (Published online August 29, 2012)
  6. Gr?tzer, G.: Lattice Theory: Foundation. Birkh?user, Basel (2011)
  7. Gr?tzer, G.: Congruences of fork extensions of slim, planar, semimodular lattices. (2014, submitted); arXiv:1307.8404
  8. Gr?tzer G, Knapp E: Notes on planar semimodular lattices. I. Construction. Acta Sci. Math. (Szeged), 73, 445-62 (2007)
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  11. Gr?tzer G, Lakser H, Schmidt E.T: Congruence lattices of finite semimodular lattices. Canad. Math. Bull. 41, 290-97 (1998) CrossRef
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  14. Kelly D, Rival I: Planar lattices. Canad. J. Math. 27, 636-65 (1975) CrossRef
  
• 作者单位：Gábor Czédli (1)
  
  1. University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, Szeged, 6720, Hungary
  
• ISSN：1420-8911

文摘

Recently, G. Gr?tzer has raised an interesting problem: Which distributive lattices are congruence lattices of slim semimodular lattices? We give an eight element slim distributive lattice that cannot be represented as the congruence lattice of a slim semimodular lattice. Our lattice demonstrates the difficulty of the problem.