{"title":"关于正则模的一些新结果","authors":"L. Oftadeh, N. Amiri","doi":"10.30495/JME.V0I0.1614","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to study unitary regular modules on commutative rings with identity. Regularity accompanied by cocyclic property results in some prime-related conclusions on both modules and rings. Further to this, regularity addresses also radical property of submodules and they are related closely. This property not only affects the modules on ring $R$ but also restricts R to totally idempotent one.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some new results on regular modules\",\"authors\":\"L. Oftadeh, N. Amiri\",\"doi\":\"10.30495/JME.V0I0.1614\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to study unitary regular modules on commutative rings with identity. Regularity accompanied by cocyclic property results in some prime-related conclusions on both modules and rings. Further to this, regularity addresses also radical property of submodules and they are related closely. This property not only affects the modules on ring $R$ but also restricts R to totally idempotent one.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V0I0.1614\",\"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":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.1614","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The aim of this paper is to study unitary regular modules on commutative rings with identity. Regularity accompanied by cocyclic property results in some prime-related conclusions on both modules and rings. Further to this, regularity addresses also radical property of submodules and they are related closely. This property not only affects the modules on ring $R$ but also restricts R to totally idempotent one.
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