On the algebraicity of generalized power series
On the algebraicity of generalized power series
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论广义幂级数的代数性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
K. Kedlaya
中科院分区：
文献类型：
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作者：
K. Kedlaya
设K是一个特征为p的代数闭域，本文给出了一个反例，反驳了我们以前的一篇文章中所提出的定理，该定理要求刻画K（（t））在Hahn-Mal'cev-Neumann广义幂级数域中的积分闭包.然后，我们给出了正确的特征，在K是有限域的代数闭包的情况下，将我们之前的描述推广到有限自动机方面。我们还刻画了K（t）的积分闭包，从而推广了Christol的一个著名定理，并提出了一个可能的计算框架。我们恢复各种推论的代数广义幂级数的结构，其中之一是一个扩展的Derksen定理的零集的线性递归序列的特征p。
Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn–Mal’cev–Neumann generalized power series. We then give a corrected characterization, generalizing our earlier description in terms of finite automata in the case where K is the algebraic closure of a finite field. We also characterize the integral closure of K(t), thus generalizing a well-known theorem of Christol and suggesting a possible framework for computing in this integral closure. We recover various corollaries on the structure of algebraic generalized power series; one of these is an extension of Derksen’s theorem on the zero sets of linear recurrent sequences in characteristic p.