在可数生成维度上

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2021-07-26 DOI:10.1142/s1005386721000286

M. Davoudian

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引用次数: 2

摘要

在本文中，我们引入并研究了可数生成维的概念，它是DCC概念在可数生成子模块上的Krull-like维的扩展。我们证明了Krull维数的一些基本结果对于可数生成维数是成立的。证明了[公式:见文]-模块[公式:见文]当且仅当其具有可数生成维数，且其Krull维数与可数生成维数重合时具有Krull维数。

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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On Countably Generated Dimension

In this article, we introduce and study the concept of countably generated dimension, which is a Krull-like dimension extension of the concept of DCC on countably generated submodules. We show that some of the basic results of Krull dimension are true for countably generated dimension. It is shown that an [Formula: see text]-module [Formula: see text] has Krull dimension if and only if it has countably generated dimension, and its Krull dimension and countably generated dimension coincide.

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.