n-distributivity and n-modularity in lattices
In this paper we consider some forbidden sublattices for n-distributive, but non-modular lattices. We define the new notion of n-modularity (weaker than n-distributivity). We also consider some forbidden sublattice for an n-modular lattice. We prove that n-modularity implies (n + 1)-modularity. The...
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| Datum: | 2004 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2004
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| Schriftenreihe: | Український математичний вісник |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/124620 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | n-distributivity and n-modularity in lattices / J. Skowronek-Kaziow // Український математичний вісник. — 2004. — Т. 1, № 2. — С. 273-278. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In this paper we consider some forbidden sublattices for n-distributive, but non-modular lattices. We define the new notion of n-modularity (weaker than n-distributivity). We also consider some forbidden sublattice for an n-modular lattice. We prove that n-modularity implies (n + 1)-modularity. The counter-examples for the inverse implication are shown. |
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