由多项式系数和幂级数产生的理想的湮灭性质

Int. J. Algebra Comput. Pub Date : 2022-02-07 DOI:10.1142/s0218196722500114

N. Kim, Yang Lee, M. Ziembowski

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引用次数: 0

摘要

本文研究了由满足结构方程的多项式系数和幂级数产生的理想的湮灭性质。我们首先证明，如果[公式:见文]对于多项式[公式:见文]在任何环上[公式:见文]，那么对于任何[公式:见文]，存在正整数[公式:见文]和[公式:见文]，使得[公式:见文]和[公式:见文]，无论何时[公式:见文]和[公式:见文]。接下来，我们证明了对于任意环上的幂级数[公式:见文]，如果[公式:见文]存在[公式:见文]，那么对于任意[公式:见文]，存在正整数[公式:见文]和[公式:见文]，使得[公式:见文]当[公式:见文]和[公式:见文]，[公式:见文]对于每一个[公式:见文]。

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Annihilating properties of ideals generated by coefficients of polynomials and power series

In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text], whenever [Formula: see text] and [Formula: see text]. Next we prove that if [Formula: see text] for power series [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] when [Formula: see text] and [Formula: see text], [Formula: see text] for each [Formula: see text].

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来源期刊

Int. J. Algebra Comput.

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