{"title":"关于可细化模块","authors":"B. Türkmen","doi":"10.15520/AJCEM.2014.VOL3.ISS5.6.PP48-51","DOIUrl":null,"url":null,"abstract":"We study on cofinitely (strong) refinable modules as a proper generalization of (strongly) refinable modules. In this paper various properties of these modules are developed. It is shown that (1) every (cofinite) direct summand of a (cofinitely) refinable module is (cofinitely) refinable; (2) a module is cofinitely refinable if and only if every cofinite direct summands lift modulo every submodule of ; (3) a ring is Rad-supplemen-ted and left refinable if and only if it is semiperfect; (4) a semilocal ring is a left and right artinian serial ring with if and only if every left -module is strongly refinable. 2010 Mathematics Subject Classification. 16D10,16D40. Key words and phrases. (strongly) refinable module, cofinitely (strong) refinable module, semiperfect ring","PeriodicalId":173381,"journal":{"name":"Asian Journal of Current Engineering and Maths","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"ON REFINABLE MODULES\",\"authors\":\"B. Türkmen\",\"doi\":\"10.15520/AJCEM.2014.VOL3.ISS5.6.PP48-51\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study on cofinitely (strong) refinable modules as a proper generalization of (strongly) refinable modules. In this paper various properties of these modules are developed. It is shown that (1) every (cofinite) direct summand of a (cofinitely) refinable module is (cofinitely) refinable; (2) a module is cofinitely refinable if and only if every cofinite direct summands lift modulo every submodule of ; (3) a ring is Rad-supplemen-ted and left refinable if and only if it is semiperfect; (4) a semilocal ring is a left and right artinian serial ring with if and only if every left -module is strongly refinable. 2010 Mathematics Subject Classification. 16D10,16D40. Key words and phrases. (strongly) refinable module, cofinitely (strong) refinable module, semiperfect ring\",\"PeriodicalId\":173381,\"journal\":{\"name\":\"Asian Journal of Current Engineering and Maths\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Current Engineering and Maths\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15520/AJCEM.2014.VOL3.ISS5.6.PP48-51\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Current Engineering and Maths","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15520/AJCEM.2014.VOL3.ISS5.6.PP48-51","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study on cofinitely (strong) refinable modules as a proper generalization of (strongly) refinable modules. In this paper various properties of these modules are developed. It is shown that (1) every (cofinite) direct summand of a (cofinitely) refinable module is (cofinitely) refinable; (2) a module is cofinitely refinable if and only if every cofinite direct summands lift modulo every submodule of ; (3) a ring is Rad-supplemen-ted and left refinable if and only if it is semiperfect; (4) a semilocal ring is a left and right artinian serial ring with if and only if every left -module is strongly refinable. 2010 Mathematics Subject Classification. 16D10,16D40. Key words and phrases. (strongly) refinable module, cofinitely (strong) refinable module, semiperfect ring
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