{"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}
引用次数: 2
Abstract
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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