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A characterization of the Jacobson radical in ternary algebras


Author: Hyo Chul Myung
Journal: Proc. Amer. Math. Soc. 38 (1973), 228-234
MSC: Primary 16A78; Secondary 17E05
DOI: https://doi.org/10.1090/S0002-9939-1973-0335582-5
MathSciNet review: 0335582
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Abstract: The Jacobson radical Rad $ T$ for a ternary algebra $ T$ is characterized as one of the following: (i) the set of properly quasi-invertible elements in $ T$; (ii) the set of $ x \in T$ such that the principal right ideal $ \left\langle {xTT} \right\rangle $ or left ideal $ \left\langle {TTx} \right\rangle $ is quasi-regular in $ T$; (iii) the unique maximal quasi-regular ideal in $ T$; (iv) the set of $ x \in T$ such that Rad $ {T^{(x)}} = {T^{(x)}}$. We also obtain ternary algebra-analogs of characterization of the radicals of certain subalgebras in an associative algebra.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0335582-5
Keywords: $ \tau $-algebra, Jacobson radical, enveloping algebra, properly quasi-invertible, quasi-regular, Jordan triple system
Article copyright: © Copyright 1973 American Mathematical Society

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