{"title":"串行模块直接求和","authors":"Alhousseynou Ba, M. A. Diompy, A. S. Diabang","doi":"10.29020/nybg.ejpam.v17i1.4973","DOIUrl":null,"url":null,"abstract":"Let R be an associative ring and M a unitary left R-module. An R-module M is said to be uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum of uniserial modules. In this paper, we bring our modest contribution to the open problem listed in the book of Alberto Facchini \"Module Theory\" which states that is any direct summand of a serial module serial? The answer is yes for particular rings and R-modules. ","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Direct Summand of Serial Modules\",\"authors\":\"Alhousseynou Ba, M. A. Diompy, A. S. Diabang\",\"doi\":\"10.29020/nybg.ejpam.v17i1.4973\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be an associative ring and M a unitary left R-module. An R-module M is said to be uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum of uniserial modules. In this paper, we bring our modest contribution to the open problem listed in the book of Alberto Facchini \\\"Module Theory\\\" which states that is any direct summand of a serial module serial? The answer is yes for particular rings and R-modules. \",\"PeriodicalId\":51807,\"journal\":{\"name\":\"European Journal of Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29020/nybg.ejpam.v17i1.4973\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29020/nybg.ejpam.v17i1.4973","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
假设 R 是一个关联环，M 是一个单元左 R 模块。如果 R 模块 M 的子模块通过包含线性有序，则称其为单列模块。序列模块是单列模块的直接和。阿尔贝托-法奇尼在《模块理论》一书中提出了一个悬而未决的问题：序列模块的任何直接和都是序列的吗？对于特定的环和 R 模块，答案是肯定的。
Let R be an associative ring and M a unitary left R-module. An R-module M is said to be uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum of uniserial modules. In this paper, we bring our modest contribution to the open problem listed in the book of Alberto Facchini "Module Theory" which states that is any direct summand of a serial module serial? The answer is yes for particular rings and R-modules.
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