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Transactions of the American Mathematical Society

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Jordan rings with involution


Author: Seong Nam Ng
Journal: Trans. Amer. Math. Soc. 200 (1974), 111-139
MSC: Primary 17C10
MathSciNet review: 0399198
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Abstract: Let $ J$ be a Jordan ring with involution $ \ast $ in which $ 2x = 0$ implies $ x = 0$ and in which $ 2J = J$. Let the set $ S$ of symmetric elements of $ J$ be periodic and let $ N$ be the Jacobson radical of $ J$. Then $ {N^2} = 0$ and $ J/N$ is a subdirect sum of $ \ast $-simple Jordan rings of the following types (1) a periodic field, (2) a direct sum of two simple periodic Jordan rings with exchange involution, (3) a $ 3 \times 3$ or $ 4 \times 4$ Jordan matrix algebra over a periodic field, (4) a Jordan algebra of a nondegenerate symmetric bilinear form on a vector space over a periodic field.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0399198-2
Article copyright: © Copyright 1974 American Mathematical Society