{"title":"其完全不变闭子模块为直接求和的模块","authors":"Enas Mustafa Kamil, Haneen Siraj Ibrahim","doi":"10.1007/s13370-025-01356-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, we define a module <i>H</i> to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of <i>H</i> is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modules whose fully invariant ec-closed submodules are direct summands\",\"authors\":\"Enas Mustafa Kamil, Haneen Siraj Ibrahim\",\"doi\":\"10.1007/s13370-025-01356-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this article, we define a module <i>H</i> to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of <i>H</i> is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 3\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01356-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01356-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Modules whose fully invariant ec-closed submodules are direct summands
In this article, we define a module H to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of H is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.
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