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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Noncommutative Jordan division algebras

Author: Kevin McCrimmon
Journal: Trans. Amer. Math. Soc. 163 (1972), 215-224
MSC: Primary 17A15
MathSciNet review: 0320098
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Abstract: The structure theory for noncommutative Jordan algebras with chain conditions leads to the following simple algebras: (I) division algebras, (II) forms of nodal algebras, (III) algebras of generic degree two, (IV) commutative Jordan matrix algebras, (V) quasi-associative algebras. The chain condition is always satisfied in a division algebra, hence does not serve as a finiteness restriction. Consequently, the general structure of noncommutative Jordan division algebras, even commutative Jordan division algebras, is unknown. In this paper we will classify those non-commutative Jordan division algebras which are forms of algebras of types (II)-(V); this includes in particular all the finite-dimensional ones.

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Keywords: Noncommutative Jordan algebra, division algebra
Article copyright: © Copyright 1972 American Mathematical Society

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