{"title":"满足(x2, y2, x2) = 0的一元实数除法代数","authors":"K. Diaby, O. Diankha, M. Ly, A. Rochdi","doi":"10.12988/IJA.2021.91501","DOIUrl":null,"url":null,"abstract":"Let A be a real division algebra with unit-element. We show that if A satisfies (x2, y2, x2) = 0 then it is flexible, quadratic and isomorphic to either R, C, a mutation of the quaternion algebra H, or a vector isotope of the octonion algebra O. Mathematics Subject Classification: 17A35 12 Kandé Diaby, Oumar Diankha, Mamoudou Ly and Abdellatif Rochdi","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"64 1","pages":"11-15"},"PeriodicalIF":0.5000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unital real division algebras satisfying (x2, y2, x2) = 0\",\"authors\":\"K. Diaby, O. Diankha, M. Ly, A. Rochdi\",\"doi\":\"10.12988/IJA.2021.91501\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let A be a real division algebra with unit-element. We show that if A satisfies (x2, y2, x2) = 0 then it is flexible, quadratic and isomorphic to either R, C, a mutation of the quaternion algebra H, or a vector isotope of the octonion algebra O. Mathematics Subject Classification: 17A35 12 Kandé Diaby, Oumar Diankha, Mamoudou Ly and Abdellatif Rochdi\",\"PeriodicalId\":13756,\"journal\":{\"name\":\"International Journal of Algebra and Computation\",\"volume\":\"64 1\",\"pages\":\"11-15\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Algebra and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12988/IJA.2021.91501\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Algebra and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12988/IJA.2021.91501","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Unital real division algebras satisfying (x2, y2, x2) = 0
Let A be a real division algebra with unit-element. We show that if A satisfies (x2, y2, x2) = 0 then it is flexible, quadratic and isomorphic to either R, C, a mutation of the quaternion algebra H, or a vector isotope of the octonion algebra O. Mathematics Subject Classification: 17A35 12 Kandé Diaby, Oumar Diankha, Mamoudou Ly and Abdellatif Rochdi
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The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.
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