Premiers, copremiers et fibrés
Dimension des couples d'anneaux partageant un idéal
Polynomes à valeurs entières sur un anneau non analytiquement irréductible.
Dimension de l'anneau des polynomes a valeurs entieres.
Anneaux presque intégralement clos
Polynômes et dérivées à valeurs entières
Polynomes a Valeurs entieres sur un anneau de Pseudovaluation.
On the ultrametric Stone-Weierstrass theorem and Mahler's expansion
We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If is a subset of a rank-one valuation domain , we show that the ring of polynomial functions is dense in the ring of continuous functions from to if and only if the topological closure of in the completion of is compact. We then show how to expand continuous functions in sums of polynomials.
Newton and Schinzel sequences in quadratic fields
We give the maximal length of a Newton or a Schinzel sequence in a quadratic extension of a global field. In the case of a number field, the maximal length of a Schinzel sequence is 1, except in seven particular cases, and the Newton sequences are also finite, except for at most finitely many cases, all real. We give the maximal length of these sequences in the special cases. We have similar results in the case of a quadratic extension of a function field , taking in account that the ring of integers...
Intégrité du complété et théorème de Stone-Weierstrass
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