{"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}
引用次数: 0
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.
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