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A valuation theory for nonassociative quaternion algebras

Kauta, John S. (2007) A valuation theory for nonassociative quaternion algebras. Communications in Algebra, 35 (11). pp. 3566-3589. ISSN 0092-7872

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      Abstract

      A nonassociative quaternion algebra over a field F is a 4-dimensional F-algebra A whose nucleus is a separable quadratic extension field of F. We define the notion of a valuation ring for A, and we also define a value function on A with values from a totally ordered group. We determine the structure of the set on which the function assumes non-negative values and we prove that, given a valuation ring of A, there is a value function associated to it if and only if the valuation ring is integral and invariant under proper F-automorphisms of A.

      Item Type: Journal Article
      Subjects: Q Science > QA Mathematics
      Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Engineering and Physics
      Depositing User: John Kauta
      Date Deposited: 06 Nov 2013 11:53
      Last Modified: 06 Nov 2013 11:53
      URI: http://repository.usp.ac.fj/id/eprint/7013
      UNSPECIFIED

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