Abstract

We investigate the properties of periodic rings R in view of studying general skew polynomials $f(t)\in R[t;\sigma ,\delta ]$. We introduce exponents for these polynomials and give some properties of this notion. We show, in particular, that this notion is right-left symmetric. Using the skew evaluation, we generalize the classical connection between the exponent of a polynomial and the order of its companion matrix.

中文翻译：

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周期环上偏多项式的指数

抽象的

考虑到一般的偏斜多项式，我们研究了周期环R的性质$F（Ť）\in \mathrm{[R}[Ť;\sigma ，\delta ]$。我们介绍这些多项式的指数，并给出该概念的一些性质。我们特别表明，该概念是左右对称的。使用偏斜评估，我们可以将多项式的指数与其伴随矩阵的阶数之间的经典关系概括化。