关于广义krull幂级数环

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2018-01-01 DOI:10.4134/BKMS.b170233

T. Le, T. Phan

{"title":"关于广义krull幂级数环","authors":"T. Le, T. Phan","doi":"10.4134/BKMS.b170233","DOIUrl":null,"url":null,"abstract":"Let R be an integral domain. We prove that the power series ring R[[X]] is a Krull domain if and only if R[[X]] is a generalized Krull domain and t-dimR ≤ 1, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts “Krull domain” and “generalized Krull domain” are the same in power series rings, (2) there exists a non-t-SFT domain R with t-dimR > 1 such that t-dimR[[X]] = 1.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"55 1","pages":"1007-1012"},"PeriodicalIF":0.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON GENERALIZED KRULL POWER SERIES RINGS\",\"authors\":\"T. Le, T. Phan\",\"doi\":\"10.4134/BKMS.b170233\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be an integral domain. We prove that the power series ring R[[X]] is a Krull domain if and only if R[[X]] is a generalized Krull domain and t-dimR ≤ 1, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts “Krull domain” and “generalized Krull domain” are the same in power series rings, (2) there exists a non-t-SFT domain R with t-dimR > 1 such that t-dimR[[X]] = 1.\",\"PeriodicalId\":55301,\"journal\":{\"name\":\"Bulletin of the Korean Mathematical Society\",\"volume\":\"55 1\",\"pages\":\"1007-1012\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/BKMS.b170233\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/BKMS.b170233","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设R是一个积分域。证明幂级数环R[[X]]是一个Krull定域当且仅当R[[X]]是一个广义Krull定域且t-dimR≤1，改进了Paran和Temkin的一个著名结果。因此，我们证明了以下一个命题成立:(1)“Krull域”和“广义Krull域”在幂级数环上是相同的概念，(2)存在一个t-dimR > 1的非t- sft域R，使得t-dimR[[X]] = 1。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

ON GENERALIZED KRULL POWER SERIES RINGS

Let R be an integral domain. We prove that the power series ring R[[X]] is a Krull domain if and only if R[[X]] is a generalized Krull domain and t-dimR ≤ 1, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts “Krull domain” and “generalized Krull domain” are the same in power series rings, (2) there exists a non-t-SFT domain R with t-dimR > 1 such that t-dimR[[X]] = 1.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).