{"title":"Valuation, weak global dimension and semihereditary in amalgamated algebra along an ideal","authors":"M. A. S. Moutui","doi":"10.12816/0006191","DOIUrl":null,"url":null,"abstract":"Let f : A! B be a ring homomorphism and J be an ideal of B. In this paper, we give a characterization of valuation, weak global dimension and semihereditary properties under a certain ring-theoretic construction called the amalgamation of A with B along J with respect to f (denoted by A ./ f J); introduced and studied by D’Anna, Finocchiaro and Fontana in 2009. Our aim is to generated new classes of commutative rings satisfying theses properties.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Open Problems in Computer Science and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12816/0006191","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
Let f : A! B be a ring homomorphism and J be an ideal of B. In this paper, we give a characterization of valuation, weak global dimension and semihereditary properties under a certain ring-theoretic construction called the amalgamation of A with B along J with respect to f (denoted by A ./ f J); introduced and studied by D’Anna, Finocchiaro and Fontana in 2009. Our aim is to generated new classes of commutative rings satisfying theses properties.
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