{"title":"包含刚性单元的抽象Witt环的结构定理","authors":"Rik Bos","doi":"10.1016/S1385-7258(89)80022-8","DOIUrl":null,"url":null,"abstract":"<div><p>Suppose (<em>R, G</em>) is a non-reduced abstract Witt ring containing a rigid element <em>d</em> such that the value set D<1,-<em>d</em>> satisfies a certain finiteness-condition. Then (<em>R, G</em>) is a direct product of a reduced abstract Witt ring and a Witt-group ring.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 125-140"},"PeriodicalIF":0.0000,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80022-8","citationCount":"1","resultStr":"{\"title\":\"A structure theorem for abstract Witt rings containing rigid elements\",\"authors\":\"Rik Bos\",\"doi\":\"10.1016/S1385-7258(89)80022-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Suppose (<em>R, G</em>) is a non-reduced abstract Witt ring containing a rigid element <em>d</em> such that the value set D<1,-<em>d</em>> satisfies a certain finiteness-condition. Then (<em>R, G</em>) is a direct product of a reduced abstract Witt ring and a Witt-group ring.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"92 2\",\"pages\":\"Pages 125-140\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80022-8\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1385725889800228\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800228","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A structure theorem for abstract Witt rings containing rigid elements
Suppose (R, G) is a non-reduced abstract Witt ring containing a rigid element d such that the value set D<1,-d> satisfies a certain finiteness-condition. Then (R, G) is a direct product of a reduced abstract Witt ring and a Witt-group ring.
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