{"title":"一个不是欧几里得定义域的主理想定义域的初等证明","authors":"Mohssin Zarouali-Darkaoui","doi":"10.12988/IMF.2019.9312","DOIUrl":null,"url":null,"abstract":"In this note we provide an elementary proof of the fact that the ring Z[(1 + i √ 19)/2] is a principal ideal domain which is not an Euclidean domain. Mathematics Subject Classification: 13F07, 13F10","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An elementary proof of a principal ideal domain which is not an Euclidean domain\",\"authors\":\"Mohssin Zarouali-Darkaoui\",\"doi\":\"10.12988/IMF.2019.9312\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we provide an elementary proof of the fact that the ring Z[(1 + i √ 19)/2] is a principal ideal domain which is not an Euclidean domain. Mathematics Subject Classification: 13F07, 13F10\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/IMF.2019.9312\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/IMF.2019.9312","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An elementary proof of a principal ideal domain which is not an Euclidean domain
In this note we provide an elementary proof of the fact that the ring Z[(1 + i √ 19)/2] is a principal ideal domain which is not an Euclidean domain. Mathematics Subject Classification: 13F07, 13F10
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