论文标题
通过线性复发关系确定的广义功率序列
Generalised power series determined by linear recurrence relations
论文作者
论文摘要
在1882年，克罗内克（Kronecker）确定，当且仅当该系列的系数满足线性复发关系时，就可以将给定的单变量的形式朗朗序列表示为两个单变量多项式的一部分。我们介绍了功率系列的广义线性复发关系的概念，其中包括任意有序的Abelian组中的指数，并概括了Kronecker的最初结果。特别是，我们获得了确定多元形式的月桂系列是否位于相应多项式环的分数场中的标准。此外，我们研究了功率系列场的区分代数子结构，该代数由广义线性复发关系决定。特别是，我们确定了一般的线性复发关系，这些关系确定了满足其他特性的功率序列字段，这对于研究其自身形态群体至关重要。
In 1882, Kronecker established that a given univariate formal Laurent series over a field can be expressed as a fraction of two univariate polynomials if and only if the coefficients of the series satisfy a linear recurrence relation. We introduce the notion of generalised linear recurrence relations for power series with exponents in an arbitrary ordered abelian group, and generalise Kronecker's original result. In particular, we obtain criteria for determining whether a multivariate formal Laurent series lies in the fraction field of the corresponding polynomial ring. Moreover, we study distinguished algebraic substructures of a power series field, which are determined by generalised linear recurrence relations. In particular, we identify generalised linear recurrence relations that determine power series fields satisfying additional properties which are essential for the study of their automorphism groups.
