在可数生成维度上

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。

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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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