Israel Journal of Mathematics

, Volume 155, Issue 1, pp 125–147 | Cite as

Nonassociative quaternion algebras over rings

  • S. Pumplün
  • V. Astier


Non-split nonassociative quaternion algebras over fields were first discovered over the real numbers independently by Dickson and Albert. They were later classified over arbitrary fields by Waterhouse. These algebras naturally appeared as the most interesting case in the classification of the four-dimensional nonassociative algebras which contain a separable field extension of the base field in their nucleus. We investigate algebras of constant rank 4 over an arbitrary ringR which contain a quadratic étale subalgebraS overR in their nucleus. A generalized Cayley-Dickson doubling process is introduced to construct a special class of these algebras.


Zero Divisor Quaternion Algebra Constant Rank Composition Algebra Principal Ideal Domain 
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Copyright information

© Hebrew University 2006

Authors and Affiliations

  • S. Pumplün
    • 1
  • V. Astier
    • 1
  1. 1.School of MathematicsUniversity of NottinghamNottinghamUK

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