Generic reducing fields of Jordan pairs

Petersson, Holger P.

doi:10.1090/S0002-9947-1984-0752505-7

Generic reducing fields of Jordan pairs
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Trans. Amer. Math. Soc. 285 (1984), 825-843 Request permission

Abstract:

Generic reducing fields of Jordan pairs, generalizing at the same time generic splitting fields of associative algebras and generic zero fields of quadratic forms, are intrinsically defined and constructed. The most elementary properties are derived, and the relationship with other generic constructions, particularly those linked to Brauer-Severi varieties, are investigated. As an application it is shown that there exist nonisomorphic exceptional Jordan division algebras having the same splitting fields.

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Über reguläre Jordan-Algebren und eine Äquivalenzrelation von

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