DC Field | Value | Language |
---|---|---|
dc.contributor.author | Phan Thanh Toan | - |
dc.contributor.author | Kang, Byung Gyun | - |
dc.date.accessioned | 2021-06-01T04:50:42Z | - |
dc.date.available | 2021-06-01T04:50:42Z | - |
dc.date.created | 2020-09-27 | - |
dc.date.issued | 2020-11 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/105533 | - |
dc.description.abstract | An ideal I of a commutative ring R with identity is called an SFT (strong finite type) ideal if there exist a finitely generated ideal J of R with J subset of I and a positive integer k such that a(k) is an element of J for each a is an element of I. A ring R is called an SFT ring if every ideal of R is an SFT ideal. Arnold showed that if R is a non-SFT ring, then the Krull dimension of the power series ring R[X] is infinite. Let C be the class of non-SFT rings. In this paper, we show that dim R[X] >= 2(N1) for every R is an element of C. In other words, if R is a non-SFT ring, then there exists a chain of prime ideals in R[X] with length at least 2(N1). We also prove that under the continuum hypothesis 2(N1) is the greatest lower bound of dim R[X] for R is an element of C. If M is a non-SFT maximal ideal of a ring R such that M is the radical of a countably generated ideal, then we construct a chain {P-alpha} of prime ideals in R[X] with length at least 2(N1) lying between MR[X] and M[X], i.e., MR[X] subset of P-alpha subset of M[X] for each alpha. The same result holds when M is the non-SFT maximal ideal of a zero-dimensional quasi-local ring or a one-dimensional quasi-local domain R. (C) 2020 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 | - |
dc.type | Article | - |
dc.identifier.doi | 10.1016/j.jalgebra.2020.06.028 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | JOURNAL OF ALGEBRA, v.562, pp.306 - 322 | - |
dc.identifier.wosid | 000562957800012 | - |
dc.citation.endPage | 322 | - |
dc.citation.startPage | 306 | - |
dc.citation.title | JOURNAL OF ALGEBRA | - |
dc.citation.volume | 562 | - |
dc.contributor.affiliatedAuthor | Kang, Byung Gyun | - |
dc.identifier.scopusid | 2-s2.0-85088040377 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | SFT PROPERTY | - |
dc.subject.keywordPlus | THEOREM | - |
dc.subject.keywordAuthor | Krull dimension | - |
dc.subject.keywordAuthor | Non-SFT ring | - |
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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