关于模块的中山特性

IF 0.8 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal Pub Date : 2023-12-12 DOI:10.1515/gmj-2023-2102

Somayeh Karimzadeh, Esmaeil Rostami, Somayeh Hadjirezaei

{"title":"关于模块的中山特性","authors":"Somayeh Karimzadeh, Esmaeil Rostami, Somayeh Hadjirezaei","doi":"10.1515/gmj-2023-2102","DOIUrl":null,"url":null,"abstract":"In this paper, we thoroughly study the Nakayama property and some related concepts. Also, we describe multiplication modules that, among other things, satisfy the Nakayama property. Next, we show that a ring 𝑅 is a Max ring if and only if all modules that can be generated by a finite or countable set have the weak Nakayama property. We prove that a ring 𝑅 is a perfect ring if and only if every module that can be generated by a finite or countable set has the Nakayama property. Finally, we present some categorical results on the aforementioned properties.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"174 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Concerning the Nakayama property of a module\",\"authors\":\"Somayeh Karimzadeh, Esmaeil Rostami, Somayeh Hadjirezaei\",\"doi\":\"10.1515/gmj-2023-2102\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we thoroughly study the Nakayama property and some related concepts. Also, we describe multiplication modules that, among other things, satisfy the Nakayama property. Next, we show that a ring 𝑅 is a Max ring if and only if all modules that can be generated by a finite or countable set have the weak Nakayama property. We prove that a ring 𝑅 is a perfect ring if and only if every module that can be generated by a finite or countable set has the Nakayama property. Finally, we present some categorical results on the aforementioned properties.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":\"174 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2023-2102\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2102","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们深入研究了中山性质和一些相关概念。此外，我们还描述了满足中山性质的乘法模块。接下来，我们证明，当且仅当所有可由有限集或可数集生成的模块都具有弱中山性质时，环𝑅 才是麦克斯环。我们证明，当且仅当每个可由有限集或可数集生成的模块都具有中山性质时，环𝑅 是完美环。最后，我们给出了上述性质的一些分类结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Concerning the Nakayama property of a module

In this paper, we thoroughly study the Nakayama property and some related concepts. Also, we describe multiplication modules that, among other things, satisfy the Nakayama property. Next, we show that a ring 𝑅 is a Max ring if and only if all modules that can be generated by a finite or countable set have the weak Nakayama property. We prove that a ring 𝑅 is a perfect ring if and only if every module that can be generated by a finite or countable set has the Nakayama property. Finally, we present some categorical results on the aforementioned properties.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Georgian Mathematical Journal 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.