{"title":"完全正二次扩展下的场不变量","authors":"E.A.M. Hornix","doi":"10.1016/S1385-7258(88)80008-8","DOIUrl":null,"url":null,"abstract":"<div><p><em>K</em> = F(√d) is a formally real field and a totally positive quadratic extension of <em>F</em>. A decomposition theorem for quadratic forms in Fed (<em>K</em>) is given. The invariants <em>r(q)</em> and <em>ud(KF)</em> are defined and relations between the invariants <em>β<sub>F</sub>(i)</em>, <em>β<sub>K</sub>(i)</em>, <em>ud(F), ud(K), l(F), l(K)</em> are studied, using the theory of quadratic forms.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 277-291"},"PeriodicalIF":0.0000,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80008-8","citationCount":"2","resultStr":"{\"title\":\"Field invariants under totally positive quadratic extensions\",\"authors\":\"E.A.M. Hornix\",\"doi\":\"10.1016/S1385-7258(88)80008-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><em>K</em> = F(√d) is a formally real field and a totally positive quadratic extension of <em>F</em>. A decomposition theorem for quadratic forms in Fed (<em>K</em>) is given. The invariants <em>r(q)</em> and <em>ud(KF)</em> are defined and relations between the invariants <em>β<sub>F</sub>(i)</em>, <em>β<sub>K</sub>(i)</em>, <em>ud(F), ud(K), l(F), l(K)</em> are studied, using the theory of quadratic forms.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"91 3\",\"pages\":\"Pages 277-291\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80008-8\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1385725888800088\",\"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/S1385725888800088","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
K = F(√d)是一个形式实域，是F的一个完全正的二次型扩展。利用二次型理论，定义了不变量r(q)和ud(KF)，研究了不变量βF(i)、βK(i)、ud(F)、ud(K)、l(F)、l(K)之间的关系。
Field invariants under totally positive quadratic extensions
K = F(√d) is a formally real field and a totally positive quadratic extension of F. A decomposition theorem for quadratic forms in Fed (K) is given. The invariants r(q) and ud(KF) are defined and relations between the invariants βF(i), βK(i), ud(F), ud(K), l(F), l(K) are studied, using the theory of quadratic forms.
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