{"title":"通过c闭子模块对ECS-模块的一般化","authors":"Enas Mustafa Kamil, Bijan Davvaz","doi":"10.1007/s13370-025-01285-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we present a new generalization of CS, ECS and CCLS- modules. If each “cec-closed submodule “in a module <i>M</i> is a “direct summand“, then <i>M</i> is referred to be CECS. It was demonstrated that every ECS and CCLS-module is generalized by the CECS property. We look at modules <i>M</i> that allow one to lift all homomorphism from a cec-closed submodule of <i>M</i> to <i>M</i>. Despite this, certain modules have some characteristics in common with CECS modules.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A generalization of ECS- modules via c-closed submodules\",\"authors\":\"Enas Mustafa Kamil, Bijan Davvaz\",\"doi\":\"10.1007/s13370-025-01285-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we present a new generalization of CS, ECS and CCLS- modules. If each “cec-closed submodule “in a module <i>M</i> is a “direct summand“, then <i>M</i> is referred to be CECS. It was demonstrated that every ECS and CCLS-module is generalized by the CECS property. We look at modules <i>M</i> that allow one to lift all homomorphism from a cec-closed submodule of <i>M</i> to <i>M</i>. Despite this, certain modules have some characteristics in common with CECS modules.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 2\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-03-25\",\"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/s13370-025-01285-x\",\"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/s13370-025-01285-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A generalization of ECS- modules via c-closed submodules
In this paper we present a new generalization of CS, ECS and CCLS- modules. If each “cec-closed submodule “in a module M is a “direct summand“, then M is referred to be CECS. It was demonstrated that every ECS and CCLS-module is generalized by the CECS property. We look at modules M that allow one to lift all homomorphism from a cec-closed submodule of M to M. Despite this, certain modules have some characteristics in common with CECS modules.
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