{"title":"沿理想的合并代数中的估值、弱全局维数和半遗传","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":"{\"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}","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
摘要
让f: A!B是环同态，J是B的理想。本文给出了a与B沿J合并的环论构造关于f(记为a ./ f . J)下的赋值、弱整体维数和半遗传性质的刻画;由D 'Anna, Finocchiaro和Fontana于2009年引入并研究。我们的目标是生成满足这些性质的交换环的新类别。
Valuation, weak global dimension and semihereditary in amalgamated algebra along an ideal
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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