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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Chain conditions on symmetric elements


Author: Susan Montgomery
Journal: Proc. Amer. Math. Soc. 46 (1974), 325-331
MSC: Primary 16A28
MathSciNet review: 0349736
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Abstract: Recently Britten has proven an analog of Goldie's theorem for the Jordan ring $ S$ of symmetric elements in a ring with involution of characteristic not 2. In this paper we first extend Britten's theorem to the situation where $ R$ is an arbitrary ring and the Jordan ring is only an ample subring of the symmetric elements. We apply this result to show that if $ S$ has ACC on quadratic ideals, then the (Jordan) nil radical of $ S$ is nilpotent.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0349736-6
PII: S 0002-9939(1974)0349736-6
Keywords: Involution, symmetric elements, Goldie ring, nil radical
Article copyright: © Copyright 1974 American Mathematical Society