主理想上满足升链条件的复合Hurwitz环

IF 0.6 Q3 MATHEMATICS Kyungpook Mathematical Journal 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。

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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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来源期刊

Kyungpook Mathematical Journal MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.