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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some structure theory for a class of triple systems


Author: Nora C. Hopkins
Journal: Trans. Amer. Math. Soc. 289 (1985), 203-212
MSC: Primary 17A40; Secondary 17A60
MathSciNet review: 779060
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Abstract: This paper deals with a class of triple systems satisfying two generalized five linear identities and having nondegenerate bilinear forms with certain properties. If $ (M,\{ ,,\} )$ is such a triple system with bilinear form $ \phi (,)$, it is shown that if $ M$ is semisimple, then $ M$ is the direct sum of simple ideals if $ \phi $ is symmetric or symplectic or if $ M$ is completely reducible as a module for its right multiplication algebra $ \mathcal{L}$. It is also shown that if $ M$ is a completely reducible $ \mathcal{L}$-module, $ M$ is the direct sum of a semisimple ideal and the center of $ M$.

Such triple systems can be embedded into certain nonassociative algebras and the results on the triple systems are extended to these algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0779060-0
PII: S 0002-9947(1985)0779060-0
Article copyright: © Copyright 1985 American Mathematical Society