Hardy type derivations on generalized series fields
| dc.contributor.author | KUHLMANN, Salma | |
| hal.structure.identifier | Équipe Géométrie | |
| dc.contributor.author | MATUSINSKI, Mickael | |
| dc.date.accessioned | 2024-04-04T02:19:42Z | |
| dc.date.available | 2024-04-04T02:19:42Z | |
| dc.date.created | 2012-02-26 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189427 | |
| dc.description.abstractEn | We consider the valued field $\mathds{K}:=\mathbb{R}((\Gamma))$ of generalized series (with real coefficients and monomials in a totally ordered multiplicative group $\Gamma$). We investigate how to endow $\mathds{K}$ with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a derivation is of Hardy type, that is, when it behaves like differentiation of germs of real valued functions in a Hardy field. We provide a necessary and sufficent condition for a series derivation of Hardy type to be surjective. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Hardy type derivations on generalized series fields | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jalgebra.2011.11.024 | |
| dc.subject.hal | Mathématiques [math]/Algèbre commutative [math.AC] | |
| dc.subject.hal | Mathématiques [math]/Logique [math.LO] | |
| dc.identifier.arxiv | 0903.2197 | |
| bordeaux.journal | Journal of Algebra | |
| bordeaux.page | 185-203 | |
| bordeaux.volume | 351 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00947040 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00947040v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Algebra&rft.date=2012&rft.volume=351&rft.issue=1&rft.spage=185-203&rft.epage=185-203&rft.eissn=0021-8693&rft.issn=0021-8693&rft.au=KUHLMANN,%20Salma&MATUSINSKI,%20Mickael&rft.genre=article |
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