{"title":"Warfield型有限生成混合模块","authors":"P. Zanardo","doi":"10.4171/rsmup/71","DOIUrl":null,"url":null,"abstract":"Let R be a local one-dimensional domain, with maximal ideal M, which is not a valuation domain. We investigate the class of the finitely generated mixed R-modules of Warfield type, so called since their construction goes back to R. B. Warfield. We prove that these R-modules have local endomorphism rings, hence they are indecomposable. We examine the torsion part t(M) of a Warfield type module M , investigating the natural property t(M) ⊂ MM . This property is related to b/a being integral over R, where a and b are elements of R that define M . We also investigate M/t(M) and determine its minimum number of generators. Mathematics Subject Classification (2010). 13G05, 13A15, 13A17.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"23 1","pages":"289-302"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finitely generated mixed modules of Warfield type\",\"authors\":\"P. Zanardo\",\"doi\":\"10.4171/rsmup/71\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be a local one-dimensional domain, with maximal ideal M, which is not a valuation domain. We investigate the class of the finitely generated mixed R-modules of Warfield type, so called since their construction goes back to R. B. Warfield. We prove that these R-modules have local endomorphism rings, hence they are indecomposable. We examine the torsion part t(M) of a Warfield type module M , investigating the natural property t(M) ⊂ MM . This property is related to b/a being integral over R, where a and b are elements of R that define M . We also investigate M/t(M) and determine its minimum number of generators. Mathematics Subject Classification (2010). 13G05, 13A15, 13A17.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"23 1\",\"pages\":\"289-302\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/71\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/71","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let R be a local one-dimensional domain, with maximal ideal M, which is not a valuation domain. We investigate the class of the finitely generated mixed R-modules of Warfield type, so called since their construction goes back to R. B. Warfield. We prove that these R-modules have local endomorphism rings, hence they are indecomposable. We examine the torsion part t(M) of a Warfield type module M , investigating the natural property t(M) ⊂ MM . This property is related to b/a being integral over R, where a and b are elements of R that define M . We also investigate M/t(M) and determine its minimum number of generators. Mathematics Subject Classification (2010). 13G05, 13A15, 13A17.
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