DC Field | Value | Language |
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dc.contributor.author | Phan Thanh Toan | - |
dc.contributor.author | Kang, Byung Gyun | - |
dc.date.accessioned | 2019-04-07T15:01:14Z | - |
dc.date.available | 2019-04-07T15:01:14Z | - |
dc.date.created | 2019-01-16 | - |
dc.date.issued | 2019-02 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/95307 | - |
dc.description.abstract | Let V be a one-dimensional nondiscrete valuation domain and let V* = V \ {0}. We prove that Krull-dimV[X](V*) >= 2(aleph 1), which is an analogue of the fact that Krull-dim E >= 2(aleph 1), where E is the ring of entire functions. The lower bound 2(aleph 1) is sharp. In fact, if V is countable then, Krull-dimV[X](V*) = 2(aleph 1 )under the continuum hypothesis. We construct a chain of prime ideals in V[X] with length >= 2(aleph 1) such that each prime ideal in the chain has height >= 2(aleph 1) and contracts to {0} in V. We also show that for a finite-dimensional valuation domain W, either Krull-dimW [X] < infinity or Krull-dimW [X] >= 2(aleph 1). (C) 2018 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.relation.isPartOf | JOURNAL OF ALGEBRA | - |
dc.title | Krull dimension of a power series ring over a valuation domain | - |
dc.type | Article | - |
dc.identifier.doi | 10.1016/j.jalgebra.2018.09.019 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | JOURNAL OF ALGEBRA, v.519, pp.62 - 86 | - |
dc.identifier.wosid | 000453635000003 | - |
dc.citation.endPage | 86 | - |
dc.citation.startPage | 62 | - |
dc.citation.title | JOURNAL OF ALGEBRA | - |
dc.citation.volume | 519 | - |
dc.contributor.affiliatedAuthor | Kang, Byung Gyun | - |
dc.identifier.scopusid | 2-s2.0-85056194000 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article | - |
dc.subject.keywordAuthor | Krull dimension | - |
dc.subject.keywordAuthor | Power series ring | - |
dc.subject.keywordAuthor | Ring of entire functions | - |
dc.subject.keywordAuthor | Ultrafilter | - |
dc.subject.keywordAuthor | Valuation domain | - |
dc.subject.keywordAuthor | eta(1)-set | - |
dc.subject.keywordAuthor | Infinite product of power series | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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