$+\infty$-$w\_0$-generated field extensions
| العنوان: | $+\infty$-$w\_0$-generated field extensions |
|---|---|
| المؤلفون: | Fliouet, El Hassane, R��sum��, Fliouet |
| سنة النشر: | 2017 |
| مصطلحات موضوعية: | FOS: Mathematics, Commutative Algebra (math.AC), Mathematics - Commutative Algebra |
| الوصف: | In this note, we continue to be interested in the relationship that connects the restricted distribution of finitude at the local level of intermediate fields of a purely inseparable extension $K/k$ to the absolute or global finitude of $K/k$. In "{\it $w\_0$-generated field extensions,}Arch. Math. {\bf 47}, (1986), 410-412", JK Deveney constructed an example of modular extension $K/k$ called $w\_0 $-generated such that for any proper subfield $L$ of $K/k $, $L$ is finite over $k$, and for every $ n \in {\mathbf N}$, we have $ [k^{p^{- n}} \cap K: k] = p^{2n} $. This example has proved to be extremely useful in the construction of other examples of $w\_0$-generated extensions. In particular, we prolong the $w\_0$-generated to an extension of unspecified finite size.However, when $K/k$ is of unbounded size, we show that any modular extension of unbounded exponent admits a proper subextension of unbounded exponent. This brings us to study the $w\_0$-generated in the restricted sense. In addition, with the aim of extending the $w\_0$-generated to a purely inseparable extension of unbounded size, we propose other generalizations. 36 pp, in French. arXiv admin note: substantial text overlap with arXiv:1701.05430 |
| اللغة: | French |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76ebce4b8672957792417bff9eba5a72 http://arxiv.org/abs/1702.02312 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....76ebce4b8672957792417bff9eba5a72 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |