DC Field | Value | Language |
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dc.contributor.author | Kang, BG | - |
dc.contributor.author | Park, MH | - |
dc.date.accessioned | 2016-03-31T08:47:22Z | - |
dc.date.available | 2016-03-31T08:47:22Z | - |
dc.date.created | 2013-02-22 | - |
dc.date.issued | 2013-03-15 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.other | 2013-OAK-0000026524 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/16052 | - |
dc.description.abstract | Let V be a rank-one nondiscrete valuation domain with maximal ideal M. We prove that the Krull-dimension of V[X](v\(0)) is uncountable, and hence the Krull-dimension of V[X] is uncountable. This corresponds to the well-known fact that the Krull-dimension of the ring of entire functions is uncountable. In fact we construct an uncountable chain of prime ideals inside M[X] such that all the members contract to (0) in V. Our method provides a new proof that the Krull-dimension of the ring of entire functions is uncountable. It is also shown that V[X](v\(0)) is not even a Prufer domain, while the ring of entire functions is a Bezout domain. These are answers to Eakin and Sathaye's questions. Applying the above results, we show that the Krull-dimension of V[X] is uncountable if V is a nondiscrete valuation domain. (C) 2012 Elsevier Inc. All rights reserved. | - |
dc.description.statementofresponsibility | X | - |
dc.language | English | - |
dc.publisher | academic press inc elsevier science | - |
dc.relation.isPartOf | journal of algebra | - |
dc.subject | Commutative ring theory | - |
dc.subject | Krull-dimension | - |
dc.subject | Power series ring | - |
dc.subject | Valuation ring | - |
dc.title | Krull dimension of a power series ring over a nondiscrete valuation domain is uncountable | - |
dc.type | Article | - |
dc.contributor.college | 수학과 | - |
dc.identifier.doi | 10.1016/J.JALGEBRA.2012.05.017 | - |
dc.author.google | Kang, BG | - |
dc.author.google | Park, MH | - |
dc.relation.volume | 378 | - |
dc.relation.startpage | 12 | - |
dc.relation.lastpage | 21 | - |
dc.contributor.id | 10053709 | - |
dc.relation.journal | journal of algebra | - |
dc.relation.index | SCI급, SCOPUS 등재논문 | - |
dc.relation.sci | SCI | - |
dc.collections.name | Journal Papers | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | journal of algebra, v.378, pp.12 - 21 | - |
dc.identifier.wosid | 000315127700002 | - |
dc.date.tcdate | 2019-01-01 | - |
dc.citation.endPage | 21 | - |
dc.citation.startPage | 12 | - |
dc.citation.title | journal of algebra | - |
dc.citation.volume | 378 | - |
dc.contributor.affiliatedAuthor | Kang, BG | - |
dc.identifier.scopusid | 2-s2.0-84872150027 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.wostc | 5 | - |
dc.description.scptc | 3 | * |
dc.date.scptcdate | 2018-05-121 | * |
dc.type.docType | Article | - |
dc.subject.keywordAuthor | Commutative ring theory | - |
dc.subject.keywordAuthor | Krull-dimension | - |
dc.subject.keywordAuthor | Power series ring | - |
dc.subject.keywordAuthor | Valuation ring | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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