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:	05 Nov 2013 22:53
Last Modified:	05 Nov 2013 22:53
URI:	https://repository.usp.ac.fj/id/eprint/7013

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