幂级数环中的除法理想 $$A+XB[\![X]\!]$$$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-18 DOI:10.1007/s40840-024-01724-1

Hamed Ahmed

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引用次数: 0

摘要

让 $A\subseteq B$ 是一个积分域的扩展，$B[\![X]\!]$ 是关于 B 的幂级数环，并且 $R=A + XB[\![X]\!]$是$B[\![X]\!].$ 在本文中，我们给出了关于 R 的 v-invertible v-ideals （在 A 中的迹不为零）的完整描述。我们证明了，如果 B 是一个完全整闭域，并且 I 是 R 的一个在 A 上有非零迹线的分数可分 v-invertible 理想，那么 $I = u(J_1 + XJ_2[\![X]\!])$ for some $u\in qf(R),$\(J_2/)是B的一个整除v-可逆理想，而（J_1/subseteq J_2/）是A的一个非零理想。

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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Divisorial Ideals in the Power Series Ring $$A+XB[\![X]\!]$$

Let $A\subseteq B$ be an extension of integral domains, $B[\![X]\!]$ be the power series ring over B, and $R=A + XB[\![X]\!]$ be a subring of $B[\![X]\!].$ In this paper, we give a complete description of v-invertible v-ideals (with nonzero trace in A) of R. We show that if B is a completely integrally closed domain and I is a fractional divisorial v-invertible ideal of R with nonzero trace over A, then $I = u(J_1 + XJ_2[\![X]\!])$ for some $u\in qf(R),$ $J_2$ an integral divisorial v-invertible ideal of B and $J_1\subseteq J_2$ a nonzero ideal of A.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.