Affiliation:
1. Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
2 articles.
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1. Dimension of uncountably generated submodules;International Electronic Journal of Algebra;2024-01-09
2. On the countably Noetherian dimension of modules;Communications in Algebra;2022-01-22