{"title":"On the kernels of higher R-derivations of R[x1,…,xn]","authors":"S. Kour","doi":"10.12958/adm1236","DOIUrl":null,"url":null,"abstract":"Let R be an integral domain and A=R [x1, . . . ,xn] be the polynomial ring innvariables. In this article, we studythe kernel of higher R-derivation D of A. It is shown that if R isa HCF ring and tr. degR (AD)⩽1 then AD=R[f] for some f ∈ A.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm1236","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Let R be an integral domain and A=R [x1, . . . ,xn] be the polynomial ring innvariables. In this article, we studythe kernel of higher R-derivation D of A. It is shown that if R isa HCF ring and tr. degR (AD)⩽1 then AD=R[f] for some f ∈ A.
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