Hardy type derivations on fields of exponential logarithmic series
| dc.contributor.author | KUHLMANN, Salma | |
| hal.structure.identifier | Équipe Géométrie | |
| dc.contributor.author | MATUSINSKI, Mickael | |
| dc.date.accessioned | 2024-04-04T02:19:40Z | |
| dc.date.available | 2024-04-04T02:19:40Z | |
| dc.date.created | 2011-09-11 | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189424 | |
| dc.description.abstractEn | We consider the valued field $\mathds{K}:=\mathbb{R}((\Gamma))$ of formal series (with real coefficients and monomials in a totally ordered multiplicative group $\Gamma>$). We investigate how to endow $\mathds{K}$ with a logarithm $l$, which satisfies some natural properties such as commuting with infinite products of monomials. In the article "Hardy type derivations on generalized series fields", we study derivations on $\mathds{K}$. Here, we investigate compatibility conditions between the logarithm and the derivation, i.e. when the logarithmic derivative is the derivative of the logarithm. We analyse sufficient conditions on a given derivation to construct a compatible logarithm via integration of logarithmic derivatives. In her monograph "Ordered exponential fields", the first author described the exponential closure $\mathds{K}^{\rm{EL}}$ of $(\mathds{K},l)$. Here we show how to extend such a log-compatible derivation on $\mathds{K}$ to $\mathds{K}^{\rm{EL}}$. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Hardy type derivations on fields of exponential logarithmic series | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jalgebra.2011.07.023 | |
| dc.subject.hal | Mathématiques [math]/Algèbre commutative [math.AC] | |
| dc.identifier.arxiv | 1010.0896 | |
| bordeaux.journal | Journal of Algebra | |
| bordeaux.page | 171-189 | |
| bordeaux.volume | 345 | |
| 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-00947059 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00947059v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Algebra&rft.date=2011&rft.volume=345&rft.issue=1&rft.spage=171-189&rft.epage=171-189&rft.eissn=0021-8693&rft.issn=0021-8693&rft.au=KUHLMANN,%20Salma&MATUSINSKI,%20Mickael&rft.genre=article |
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