{"title":"除法环的乘法群","authors":"R. Hazrat, M. Mahdavi-Hezavehi, M. Motiee","doi":"10.3318/PRIA.2014.114.04","DOIUrl":null,"url":null,"abstract":"Exactly 170 years ago, the construction of the real quaternion algebra by William Hamilton was announced in the Proceedings of the Royal Irish Academy. It became the first example of non-commutative division rings and a major turning point of algebra. To this day, the multiplicative group structure of quaternion algebras have not completely been understood. This article is a long survey of the recent developments on the multiplicative group structure of division rings.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"Multiplicative groups of division rings\",\"authors\":\"R. Hazrat, M. Mahdavi-Hezavehi, M. Motiee\",\"doi\":\"10.3318/PRIA.2014.114.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Exactly 170 years ago, the construction of the real quaternion algebra by William Hamilton was announced in the Proceedings of the Royal Irish Academy. It became the first example of non-commutative division rings and a major turning point of algebra. To this day, the multiplicative group structure of quaternion algebras have not completely been understood. This article is a long survey of the recent developments on the multiplicative group structure of division rings.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-02-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2014.114.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2014.114.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exactly 170 years ago, the construction of the real quaternion algebra by William Hamilton was announced in the Proceedings of the Royal Irish Academy. It became the first example of non-commutative division rings and a major turning point of algebra. To this day, the multiplicative group structure of quaternion algebras have not completely been understood. This article is a long survey of the recent developments on the multiplicative group structure of division rings.
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