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Division Algebras with Radicable Multiplicative Groups

Mahdavi Hezavehi, M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1080/00927872.2010.517819
  3. Abstract:
  4. Given a divisible finite field extension K/F, the structure of Br(F), the Brauer group of F, is investigated. It is shown that, if F is indivisible, then Br(F) ≅ ℤ 2, which generalizes the Frobenius Theorem. As a consequence, when F is indivisible, the class of all finite dimensional non-commutative F-central division algebras D having radicable multiplicative groups D* is determined. In fact, it is proved that the following statements are equivalent: (1) D is radicable, (2) D contains a divisible subfield K/F, and (3) D is the ordinary quaternion division algebra and F(√-1) is divisible
  5. Keywords:
  6. Divisible group ; Division algebra ; Finite field extension
  7. Source: Communications in Algebra ; Volume 39, Issue 11 , 2011 , Pages 4084-4096 ; 00927872 (ISSN)
  8. URL: http://www.tandfonline.com./doi/abs/10.1080/00927872.2010.517819