{"title":"On Countably Generated Dimension","authors":"M. Davoudian","doi":"10.1142/s1005386721000286","DOIUrl":null,"url":null,"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386721000286","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
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.
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