Dynamical method in algebra: Effective Nullstellensätze
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2017
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918007442243584 |
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| author | Coste, Michel Lombardi, Henri Roy, Marie-Françoise |
| author_facet | Coste, Michel Lombardi, Henri Roy, Marie-Françoise |
| contents | We give a general method for producing various effective Null and Positivstellensätze, and getting new Positivstellensätze in algebraically closed valued fields and ordered groups. These various effective Nullstellensätze produce algebraic identities certifying that some geometric conditions cannot be simultaneously satisfied. We produce also constructive versions of abstract classical results of algebra based on Zorn's lemma in several cases where such constructive version did not exist. For example, the fact that a real field can be totally ordered, or the fact that a field can be embedded in an algebraically closed field. Our results are based on the concepts we develop of dynamical proofs and simultaneous collapse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1701_05794 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Dynamical method in algebra: Effective Nullstellensätze Coste, Michel Lombardi, Henri Roy, Marie-Françoise Algebraic Geometry Logic 03F65, 06F15, 12J10, 12J15, 18B25 We give a general method for producing various effective Null and Positivstellensätze, and getting new Positivstellensätze in algebraically closed valued fields and ordered groups. These various effective Nullstellensätze produce algebraic identities certifying that some geometric conditions cannot be simultaneously satisfied. We produce also constructive versions of abstract classical results of algebra based on Zorn's lemma in several cases where such constructive version did not exist. For example, the fact that a real field can be totally ordered, or the fact that a field can be embedded in an algebraically closed field. Our results are based on the concepts we develop of dynamical proofs and simultaneous collapse. |
| title | Dynamical method in algebra: Effective Nullstellensätze |
| topic | Algebraic Geometry Logic 03F65, 06F15, 12J10, 12J15, 18B25 |
| url | https://arxiv.org/abs/1701.05794 |