Rado's theorem for rings and modules
| Autor: | Jakub Byszewski, Elzbieta Krawczyk |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Ring (mathematics) Noetherian ring Mathematics::Commutative Algebra 010102 general mathematics 0102 computer and information sciences Mathematics - Commutative Algebra System of linear equations Commutative Algebra (math.AC) 01 natural sciences Rado's theorem Theoretical Computer Science Integral domain Matrix (mathematics) Computational Theory and Mathematics Integer 010201 computation theory & mathematics Partition regularity FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1804.05341 |
| Popis: | We extend classical results of Rado on partition regularity of systems of linear equations with integer coefficients to the case when the coefficient ring is either an arbitrary integral domain or a noetherian ring. In particular, we show that a system of homogeneous linear equations over an infinite integral domain is partition regular if and only if the corresponding matrix satisfies the columns conditions. The crucial idea is to study partition regularity for general modules rather than only for rings. Contrary to previous techniques, our approach is independent of the characteristic of the coefficient ring. Comment: 21 pages, v2:rewritten introduction, updated references, to appear in JCTA |
| Databáze: | OpenAIRE |
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