DC Field | Value | Language |
---|---|---|
dc.contributor.author | Phan Thanh Toan | - |
dc.contributor.author | Kang, Byung Gyun | - |
dc.date.accessioned | 2019-04-07T17:57:05Z | - |
dc.date.available | 2019-04-07T17:57:05Z | - |
dc.date.created | 2018-03-19 | - |
dc.date.issued | 2018-04 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/95930 | - |
dc.description.abstract | A ring D is called an SFT ring if for each ideal I of D, there exist a finitely generated ideal J of D with J subset of I and a positive integer k such that a(k) is an element of J for all a is an element of I. For a cardinal number alpha and a ring D, we say that dim D > alpha if D has a chain of prime ideals with length >= alpha. Arnold showed that if D is a non-SFT ring, then dim D[X] >= N0. Let C be the class of non-SFT domains. The class C includes the class of finite -dimensional nondiscrete valuation domains, the class of non-Noetherian almost Dedekind domains, the class of completely integrally closed domains that are not Krull domains, the class of integral domains with non-Noetherian prime spectrum, and the class of integral domains with a nonzero proper idempotent ideal. The ring of algebraic integers, the ring of integer -valued polynomials on Z, and the ring of entire functions are also members of the class C. In this paper we prove that dim D[X] >= 2(N1) for every D is an element of C and that under the continuum hypothesis 2(N1) is the greatest lower bound of dim D[X] for D is an element of C. On the ther hand, there exists a (finite-dimensional) SFT domain D such that dim D[X] >= 2(N1). (C) 2017 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 power series rings over non-SFT domains | - |
dc.type | Article | - |
dc.identifier.doi | 10.1016/j.jalgebra.2017.12.011 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | JOURNAL OF ALGEBRA, v.499, pp.516 - 537 | - |
dc.identifier.wosid | 000425578400024 | - |
dc.citation.endPage | 537 | - |
dc.citation.startPage | 516 | - |
dc.citation.title | JOURNAL OF ALGEBRA | - |
dc.citation.volume | 499 | - |
dc.contributor.affiliatedAuthor | Kang, Byung Gyun | - |
dc.identifier.scopusid | 2-s2.0-85044853334 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | VALUATION DOMAIN | - |
dc.subject.keywordPlus | DEDEKIND DOMAINS | - |
dc.subject.keywordPlus | PRUFER DOMAINS | - |
dc.subject.keywordPlus | PROPERTY | - |
dc.subject.keywordAuthor | Krull dimension | - |
dc.subject.keywordAuthor | Non-SFT domain | - |
dc.subject.keywordAuthor | Power series ring | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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