DC Field | Value | Language |
---|---|---|
dc.contributor.author | Phan Thanh Toan | - |
dc.contributor.author | Kang, Byung Gyun | - |
dc.date.accessioned | 2018-01-04T10:38:32Z | - |
dc.date.available | 2018-01-04T10:38:32Z | - |
dc.date.created | 2017-03-10 | - |
dc.date.issued | 2017-03 | - |
dc.identifier.issn | 0035-7596 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/39179 | - |
dc.description.abstract | Let R be a commutative ring with identity, and let R[x] be the collection of polynomials with coefficients in R. We observe that there are many multiplications in R[x] such that, together with the usual addition, R[x] becomes a ring that contains R as a subring. These multiplications belong to a class of functions �� from N0 to N. The trivial case when ��(i) = 1 for all i gives the usual polynomial ring. Among nontrivial cases, there is an important one, namely, the case when ��(i) = i! for all i. For this case, it gives the well-known Hurwitz polynomial ring RH[x]. In this paper, we study Krull dimension and unique factorization in RH[x]. We show in general that dimR �� dimRH[x] �� 2 dimR + 1. When the ring R is Noetherian we prove that dimR �� dimRH[x] �� dimR + 1. A condition for the ring R is also given in order to determine whether dimRH[x] = dimR or dimRH[x] = dimR+1 in this case. We show that RH[x] is a unique factorization domain, respectively, a Krull domain, if and only if R is a unique factorization domain, respectively, a Krull domain, containing all of the rational numbers. ? 2017 Rocky Mountain Mathematics Consortium. | - |
dc.language | English | - |
dc.publisher | Rocky Mountain Mathematics Consortium | - |
dc.relation.isPartOf | Rocky Mountain Journal of Mathematics | - |
dc.title | KRULL DIMENSION AND UNIQUE FACTORIZATION IN HURWITZ POLYNOMIAL RINGS | - |
dc.type | Article | - |
dc.identifier.doi | 10.1216/RMJ-2017-47-4-1317 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | Rocky Mountain Journal of Mathematics, v.74, no.4, pp.1317 - 1332 | - |
dc.identifier.wosid | 000416899600013 | - |
dc.date.tcdate | 2019-02-01 | - |
dc.citation.endPage | 1332 | - |
dc.citation.number | 4 | - |
dc.citation.startPage | 1317 | - |
dc.citation.title | Rocky Mountain Journal of Mathematics | - |
dc.citation.volume | 74 | - |
dc.contributor.affiliatedAuthor | Kang, Byung Gyun | - |
dc.identifier.scopusid | 2-s2.0-85026882875 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.wostc | 1 | - |
dc.type.docType | ARTICLE | - |
dc.subject.keywordPlus | SERIES RING | - |
dc.subject.keywordAuthor | Hurwitz polynomial | - |
dc.subject.keywordAuthor | Krull dimension | - |
dc.subject.keywordAuthor | Noetherian ring | - |
dc.subject.keywordAuthor | polynomial ring | - |
dc.subject.keywordAuthor | unique factorization | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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