偏态多项式的指数

Ahmed Cherchem, A. Leroy
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引用次数: 5

摘要

引入了有限环中两个元素的相对指数的概念,并应用它来定义和研究了一个多项式的指数,其形式为:F q t;? . 这推广了在有限域中具有系数的多项式的指数(即阶或周期)的经典概念。通过研究有限群中元素的偏序的概念,得到了多项式的指数、根的阶和伴随矩阵的阶之间的经典联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponents of skew polynomials
We introduce the notion of a relative exponent for two elements in a finite ring and apply this to define and study the exponent of a polynomial in an Ore extension of the form F q t ; ? . This generalizes the classical notion of exponent (a.k.a. order or period) of a polynomial with coefficients in a finite field. The classical connections between the exponent of a polynomial, the order of its roots and of its companion matrix are obtained via the study of a notion of skew order of an element in a finite group.
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