DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chang, Gyu Whan | - |
dc.contributor.author | Kang, Byung Gyun | - |
dc.date.accessioned | 2019-04-07T17:57:25Z | - |
dc.date.available | 2019-04-07T17:57:25Z | - |
dc.date.created | 2018-07-20 | - |
dc.date.issued | 2018-03 | - |
dc.identifier.issn | 0092-7872 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/95935 | - |
dc.description.abstract | A ring is called an r-Noetherian ring if every regular ideal is finitely generated. Let R be an r-Noetherian ring, let / be a regular ideal of R, and let (R)over-cap be the I-adic completion of R. We show that (R)over-cap is a Noetherian ring and dim(R)over-cap = sup {r-ht(M) vertical bar M is an element of Max(R) and I subset of M}. Let P be a prime ideal of R. We also prove that for any a is an element of reg(P), r-htP = ht(P/aR) + 1 and that if P is minimal over an n-generated regular ideal, then r-htP <= n. | - |
dc.language | English | - |
dc.publisher | TAYLOR & FRANCIS INC | - |
dc.relation.isPartOf | COMMUNICATIONS IN ALGEBRA | - |
dc.title | The completion and Krull's generalized principal ideal theorem on r-Noetherian rings | - |
dc.type | Article | - |
dc.identifier.doi | 10.1080/00927872.2017.1350698 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | COMMUNICATIONS IN ALGEBRA, v.46, no.3, pp.1231 - 1236 | - |
dc.identifier.wosid | 000429054400027 | - |
dc.citation.endPage | 1236 | - |
dc.citation.number | 3 | - |
dc.citation.startPage | 1231 | - |
dc.citation.title | COMMUNICATIONS IN ALGEBRA | - |
dc.citation.volume | 46 | - |
dc.contributor.affiliatedAuthor | Kang, Byung Gyun | - |
dc.identifier.scopusid | 2-s2.0-85028801396 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | INTEGRAL CLOSURE | - |
dc.subject.keywordAuthor | Ideal-adic completion | - |
dc.subject.keywordAuthor | Krull dimension | - |
dc.subject.keywordAuthor | Krull&apos | - |
dc.subject.keywordAuthor | s generalized principal ideal theorem | - |
dc.subject.keywordAuthor | r-Noetherian ring | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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