On Countably Generated Dimension

被引：2

作者：

Davoudian, Maryam ^{[1
]}

机构：

[1] Shahid Chamran Univ Ahvaz, Dept Math, Ahvaz, Iran

来源：

ALGEBRA COLLOQUIUM | 2021年 / 28卷 / 03期

关键词：

countably generated module; Krull dimension; countably generated dimension; MODULES;

D O I：

10.1142/S1005386721000286

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 R-module M has Krull dimension if and only if it has countably generated dimension, and its Krull dimension and countably generated dimension coincide.

引用

页码：361 / 366

页数：6

共 17 条

[1] Chain conditions on quotient finite dimensional modules [J].