有限域上幂级数场的初等性质
Elementary properties of power series fields over finite fields
摘要：
尽管Q_p和F_p（（t））之间的相似性通过Ax和Kochen的工作变得明显，但将他们给出的Q_p的完整递归公理系统修改为F_p（（t））的情况并不表示一个完整的公理系统。本文证明了表示可加多项式作为映射在F_p（（t））上作用的初等性质的独立性。我们制定了一个基本的属性表示这一行动，并表明，它适用于所有的极大值领域。我们还讨论了任意多项式在值域上的作用。
英文摘要：
In spite of the analogies between Q_p and F_p((t)) which became evident through the work of Ax and Kochen, an adaptation of the complete recursive axiom system given by them for Q_p to the case of F_p((t)) does not render a complete axiom system. We show the independence of elementary properties which express the action of additive polynomials as maps on F_p((t)). We formulate an elementary property expressing this action and show that it holds for all maximal valued fields. We also discuss the action of arbitrary polynomials on valued fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
