{"title":"特征 2 中普菲斯特倍数的各向同性指数","authors":"Nico Lorenz , Kristýna Zemková","doi":"10.1016/j.jpaa.2024.107759","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>F</em> be a field of characteristic 2, <em>π</em> an <em>n</em>-fold bilinear Pfister form over <em>F</em> and <em>φ</em> an arbitrary quadratic form over <em>F</em>. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy indices of <em>φ</em> and <span><math><mi>π</mi><mo>⊗</mo><mi>φ</mi></math></span> and prove relations among the indices of these two forms over certain field extensions.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"228 12","pages":"Article 107759"},"PeriodicalIF":0.7000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001567/pdfft?md5=4a793c50fe87144e70295cee7055ed3c&pid=1-s2.0-S0022404924001567-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Isotropy indices of Pfister multiples in characteristic 2\",\"authors\":\"Nico Lorenz , Kristýna Zemková\",\"doi\":\"10.1016/j.jpaa.2024.107759\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>F</em> be a field of characteristic 2, <em>π</em> an <em>n</em>-fold bilinear Pfister form over <em>F</em> and <em>φ</em> an arbitrary quadratic form over <em>F</em>. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy indices of <em>φ</em> and <span><math><mi>π</mi><mo>⊗</mo><mi>φ</mi></math></span> and prove relations among the indices of these two forms over certain field extensions.</p></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"228 12\",\"pages\":\"Article 107759\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022404924001567/pdfft?md5=4a793c50fe87144e70295cee7055ed3c&pid=1-s2.0-S0022404924001567-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404924001567\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924001567","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Isotropy indices of Pfister multiples in characteristic 2
Let F be a field of characteristic 2, π an n-fold bilinear Pfister form over F and φ an arbitrary quadratic form over F. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy indices of φ and and prove relations among the indices of these two forms over certain field extensions.
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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