{"title":"论有限生成局部循环模块的戈尔迪维度","authors":"B. Boudine, Soibri Moindze","doi":"10.24193/mathcluj.2023.2.06","DOIUrl":null,"url":null,"abstract":"Let R be a commutative ring with identity. In this paper we investigate the Goldie dimension of finitely generated locally cyclic R-modules. Then, we give a characterization of rings whose finitely generated locally cyclics have finite Goldie dimension.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Goldie dimension of finitely generated locally cyclic modules\",\"authors\":\"B. Boudine, Soibri Moindze\",\"doi\":\"10.24193/mathcluj.2023.2.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be a commutative ring with identity. In this paper we investigate the Goldie dimension of finitely generated locally cyclic R-modules. Then, we give a characterization of rings whose finitely generated locally cyclics have finite Goldie dimension.\",\"PeriodicalId\":39356,\"journal\":{\"name\":\"Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/mathcluj.2023.2.06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/mathcluj.2023.2.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
设 R 是具有同一性的交换环。本文将研究有限生成的局部循环 R 模块的戈尔迪维度。然后，我们给出了有限生成的局部循环具有有限戈尔迪维度的环的特征。
On the Goldie dimension of finitely generated locally cyclic modules
Let R be a commutative ring with identity. In this paper we investigate the Goldie dimension of finitely generated locally cyclic R-modules. Then, we give a characterization of rings whose finitely generated locally cyclics have finite Goldie dimension.
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