关于j{mathscr{j}}-诺特环

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-17 DOI:10.1515/math-2024-0014

Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Najib Mahdou, El Houssaine Oubouhou

引用次数: 0

摘要

设 R R 是一个具有同一性的交换环，而 j {\mathscr{j}} 是 R R 的一个理想。如果 R R 的理想 I I ⊈ j I\hspace{0}} 是一个 j {\mathscr{j}} 的理想，那么这个理想就是 R R 的理想 I I 。 -理想，如果 I ⊈ j I\hspace{0.33em}\nsubseteq \hspace{0.33em}{\mathscr{j}} .我们定义 R R 是一个 j {\mathscr{j}} 。 -如果每个 j {\mathscr{j} 都是 R R 的ideal，那么 R R 就是一个 j {\mathscr{j}} 的诺特环。 -的ideal 都是有限生成的。在这项工作中，我们将研究 j {\mathscr{j}} -诺特环的一些性质。 -诺特环的一些性质。更准确地说，我们通过共振来研究 j {\mathscr{j}} -诺特环。 -Noetherian 环的科恩型定理、平延伸、可分解环、三维延伸环、合并重复、多项式环延伸和幂级数环延伸。

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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About j{\mathscr{j}}-Noetherian rings

Let

be a commutative ring with identity and

{\mathscr{j}}

an ideal of

. An ideal

is said to be a

{\mathscr{j}}

-ideal if

I ⊈ j

I\hspace{0.33em} \nsubseteq \hspace{0.33em}{\mathscr{j}}

. We define

to be a

{\mathscr{j}}

-Noetherian ring if each

{\mathscr{j}}

-ideal of

is finitely generated. In this work, we study some properties of

{\mathscr{j}}

-Noetherian rings. More precisely, we investigate

{\mathscr{j}}

-Noetherian rings via the Cohen-type theorem, the flat extension, decomposable ring, the trivial extension ring, the amalgamated duplication, the polynomial ring extension, and the power series ring extension.

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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.