{"title":"可整除性和双环","authors":"U. Albrecht, Bradley McQuaig","doi":"10.4171/rsmup/40","DOIUrl":null,"url":null,"abstract":"This paper investigates the projective dimension of the maximal right ring of quotients Q(R) of a right non-singular ring R. Our discussion addresses the question under which conditions p.d.(Q)) ≤ 1 guarantees that the module Q/R is a direct sum of countably generated modules extending Matlis’ Theorem for integral domains to a non-commutative setting. Mathematics Subject Classification (2010). Primary: 16D10; Secondary: 16D40, 16E30, 16P50, 16P60, 16S85.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"90 1","pages":"81-103"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Divisibility and duo-rings\",\"authors\":\"U. Albrecht, Bradley McQuaig\",\"doi\":\"10.4171/rsmup/40\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper investigates the projective dimension of the maximal right ring of quotients Q(R) of a right non-singular ring R. Our discussion addresses the question under which conditions p.d.(Q)) ≤ 1 guarantees that the module Q/R is a direct sum of countably generated modules extending Matlis’ Theorem for integral domains to a non-commutative setting. Mathematics Subject Classification (2010). Primary: 16D10; Secondary: 16D40, 16E30, 16P50, 16P60, 16S85.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"90 1\",\"pages\":\"81-103\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-24\",\"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/40\",\"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/40","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper investigates the projective dimension of the maximal right ring of quotients Q(R) of a right non-singular ring R. Our discussion addresses the question under which conditions p.d.(Q)) ≤ 1 guarantees that the module Q/R is a direct sum of countably generated modules extending Matlis’ Theorem for integral domains to a non-commutative setting. Mathematics Subject Classification (2010). Primary: 16D10; Secondary: 16D40, 16E30, 16P50, 16P60, 16S85.
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