Homology of Distributive Lattices
| Autor: | Krzysztof K. Putyra, Józef H. Przytycki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Conjecture High Energy Physics::Lattice 010102 general mathematics Skew Geometric Topology (math.GT) Distributive lattice 0102 computer and information sciences Absorption law Mathematics - Rings and Algebras Homology (mathematics) 16. Peace & justice 01 natural sciences Mathematics - Geometric Topology Distributive property Rings and Algebras (math.RA) 010201 computation theory & mathematics Lattice (order) Idempotence FOS: Mathematics Geometry and Topology 0101 mathematics Mathematics |
| Popis: | We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology of a finite distributive lattice. We also indicate the answer for unital spindles and conjecture the general formula for semi-lattices and some skew lattices. Then we propose a generalization of a lattice as a set with a number of idempotent operations satisfying the absorption law. 30 pages, 3 tables, 3 figures |
| Databáze: | OpenAIRE |
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