{"title":"统一阿尔丁环和模块的一些经典结果","authors":"Donovan Leyba, Zachary Mesyan, Greg Oman","doi":"10.1080/00927872.2024.2389949","DOIUrl":null,"url":null,"abstract":"In this note, we introduce a very crude but natural notion of measure on the class of left R-modules over a ring R. We use this notion to give short proofs of some classical theorems on (left) Arti...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"30 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unifying some classical results on Artinian rings and modules\",\"authors\":\"Donovan Leyba, Zachary Mesyan, Greg Oman\",\"doi\":\"10.1080/00927872.2024.2389949\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we introduce a very crude but natural notion of measure on the class of left R-modules over a ring R. We use this notion to give short proofs of some classical theorems on (left) Arti...\",\"PeriodicalId\":50663,\"journal\":{\"name\":\"Communications in Algebra\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/00927872.2024.2389949\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00927872.2024.2389949","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Unifying some classical results on Artinian rings and modules
In this note, we introduce a very crude but natural notion of measure on the class of left R-modules over a ring R. We use this notion to give short proofs of some classical theorems on (left) Arti...
期刊介绍：
Communications in Algebra presents high quality papers of original research in the field of algebra. Articles from related research areas that have a significant bearing on algebra might also be published.
Topics Covered Include:
-Commutative Algebra
-Ring Theory
-Module Theory
-Non-associative Algebra including Lie algebras, Jordan algebras
-Group Theory
-Algebraic geometry
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