A new property of congruence lattices of slim, planar, semimodular lattices
The systematic study of planar semimodular lattices started in2007 with a series of papers by G. Grätzer and E. Knapp. These lattices haveconnections with group theory and geometry. A planar semimodular latticeL is slim if M3 it is not a sublattice of L. In his 2016 monograph, “TheCongruences of a F...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2022-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | https://cgasa.sbu.ac.ir/article_101508_ad42a5d1a69a3f6cc445ec82aaffc367.pdf |
| _version_ | 1818331762665717760 |
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| author | Gábor Cz´edli George Gr¨atzer |
| author_facet | Gábor Cz´edli George Gr¨atzer |
| author_sort | Gábor Cz´edli |
| collection | DOAJ |
| description | The systematic study of planar semimodular lattices started in2007 with a series of papers by G. Grätzer and E. Knapp. These lattices haveconnections with group theory and geometry. A planar semimodular latticeL is slim if M3 it is not a sublattice of L. In his 2016 monograph, “TheCongruences of a Finite Lattice, A Proof-by-Picture Approach”, the secondauthor asked for a characterization of congruence lattices of slim, planar,semimodular lattices. In addition to distributivity, both authors have previouslyfound specific properties of these congruence lattices. In this paper,we present a new property, the Three-pendant Three-crown Property. Theproof is based on the first author’s papers: 2014 (multifork extensions), 2017(C1-diagrams), and a recent paper (lamps), introducing the tools we need. |
| first_indexed | 2024-12-13T13:25:00Z |
| format | Article |
| id | doaj.art-5e43e666c9b84e2db98b48c10ab70e8e |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-13T13:25:00Z |
| publishDate | 2022-01-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-5e43e666c9b84e2db98b48c10ab70e8e2022-12-21T23:44:19ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612022-01-0116112810.52547/cgasa.2021.101508101508A new property of congruence lattices of slim, planar, semimodular latticesGábor Cz´edli0George Gr¨atzer1Bolyai Institute, University of Szeged, Szeged, Aradi H6720 HungaryUniversity of Manitoba, CanadaThe systematic study of planar semimodular lattices started in2007 with a series of papers by G. Grätzer and E. Knapp. These lattices haveconnections with group theory and geometry. A planar semimodular latticeL is slim if M3 it is not a sublattice of L. In his 2016 monograph, “TheCongruences of a Finite Lattice, A Proof-by-Picture Approach”, the secondauthor asked for a characterization of congruence lattices of slim, planar,semimodular lattices. In addition to distributivity, both authors have previouslyfound specific properties of these congruence lattices. In this paper,we present a new property, the Three-pendant Three-crown Property. Theproof is based on the first author’s papers: 2014 (multifork extensions), 2017(C1-diagrams), and a recent paper (lamps), introducing the tools we need.https://cgasa.sbu.ac.ir/article_101508_ad42a5d1a69a3f6cc445ec82aaffc367.pdfrectangular latticepatch latticeslim semimodular latticecongruence latticelattice congruencethree-pendant three-crown property |
| spellingShingle | Gábor Cz´edli George Gr¨atzer A new property of congruence lattices of slim, planar, semimodular lattices Categories and General Algebraic Structures with Applications rectangular lattice patch lattice slim semimodular lattice congruence lattice lattice congruence three-pendant three-crown property |
| title | A new property of congruence lattices of slim, planar, semimodular lattices |
| title_full | A new property of congruence lattices of slim, planar, semimodular lattices |
| title_fullStr | A new property of congruence lattices of slim, planar, semimodular lattices |
| title_full_unstemmed | A new property of congruence lattices of slim, planar, semimodular lattices |
| title_short | A new property of congruence lattices of slim, planar, semimodular lattices |
| title_sort | new property of congruence lattices of slim planar semimodular lattices |
| topic | rectangular lattice patch lattice slim semimodular lattice congruence lattice lattice congruence three-pendant three-crown property |
| url | https://cgasa.sbu.ac.ir/article_101508_ad42a5d1a69a3f6cc445ec82aaffc367.pdf |
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