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The Arithmetics of Quadratic Jordan Algebras
Michel L. Racine
出版American Mathematical Soc., 1973
主題Mathematics / GeneralMathematics / Algebra / Abstract
ISBN08218183689780821818367
URLhttp://books.google.com.hk/books?id=69_TCQAAQBAJ&hl=&source=gbs_api
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註釋The first step in obtaining an arithmetic theory for finite dimensional quadratic Jordan algebras over the quotient field of a Dedekind ring is the determination of maximal orders. This is the main concern of this paper. Jordan analogues of some of the first theorems in classical associative arithmetic are obtained. For special quadratic Jordan algebras, the problem of determining maximal orders is reduced to arithmetic questions in quadratic forms and associative algebras with involution. The number of isomorphism classes of maximal orders is computed for most central simple quadratic Jordan algebras over a local field. In the process, previous results of Knebusch are obtained in a uniform fashion and are extended to the case of algebras over fields of characteristic 2 and 3.