{"title":"关于复合代数的Hurwit'z定理的证明","authors":"Aleksandra Galecka","doi":"10.24917/20809751.13.4","DOIUrl":null,"url":null,"abstract":"We present a proof of the Hurwitz Theorem about construction and properties of real numbers, complex numbers, quaternions and octonions. In the proof we use the Dickson double for Cayley-Dickson algebras.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Proof of the Hurwit'z Theorem About Composition Algebras\",\"authors\":\"Aleksandra Galecka\",\"doi\":\"10.24917/20809751.13.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a proof of the Hurwitz Theorem about construction and properties of real numbers, complex numbers, quaternions and octonions. In the proof we use the Dickson double for Cayley-Dickson algebras.\",\"PeriodicalId\":33912,\"journal\":{\"name\":\"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae\",\"volume\":\"42 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24917/20809751.13.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24917/20809751.13.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Proof of the Hurwit'z Theorem About Composition Algebras
We present a proof of the Hurwitz Theorem about construction and properties of real numbers, complex numbers, quaternions and octonions. In the proof we use the Dickson double for Cayley-Dickson algebras.
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