主理想上满足升链条件的复合Hurwitz环

Pub Date : 2016-12-23 DOI:10.5666/KMJ.2016.56.4.1115

J. Lim, D. Y. Oh

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引用次数: 4

摘要

设D≤E是特征为0的整域的扩展，I为D的非零本理想，设H(D,E)和H(D, I) (， h(D,E)和h(D, I))为复合Hurwitz级数环(，复合Hurwitz多项式环)。本文证明了H(D,E)满足主理想上的升链条件，当且仅当H(D,E)满足主理想上的升链条件，当且仅当∩n≥1 a1···anE =(0)对于由D的非零非单位组成的无限序列(an)n≥1，我们还证明了H(D, I)满足主理想上的升链条件当且仅当H(D, I)满足主理想上的升链条件。当且仅当D满足主理想上的升链条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Composite Hurwitz Rings Satisfying the Ascending Chain Condition on Principal Ideals

Let D ⊆ E be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D and let H(D,E) and H(D, I) (resp., h(D,E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this paper, we show that H(D,E) satisfies the ascending chain condition on principal ideals if and only if h(D,E) satisfies the ascending chain condition on principal ideals, if and only if ∩ n≥1 a1 · · · anE = (0) for each infinite sequence (an)n≥1 consisting of nonzero nonunits of D. We also prove that H(D, I) satisfies the ascending chain condition on principal ideals if and only if h(D, I) satisfies the ascending chain condition on principal ideals, if and only if D satisfies the ascending chain condition on principal ideals.

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