{"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}
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.
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).
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