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On the Levitzki Radical

Published online by Cambridge University Press:  20 November 2018

Tim Anderson
Tim Anderson*
Affiliation:
University of British Columbia
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The Levitzki radical, which is fundamental in the study of algebras satisfying a polynomial identity, has been shown to exist in the varieties of alternative and Jordan algebras (see Zhevlakov [8], Zwier [9], and Tsai [7]— for an important application of this radical to alternative algebras satisfying a polynomial identity, see Slater [6]). In fact, Hartley [4] even investigated local nilpotence for Lie algebras, though this property can not be radical in the sense of Kurosh-Amitsur [3] for these algebras.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 5 - 10
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Albert, A. A., Almost alternative algebras, Port. Math. 8 (1949), 23-36.Google Scholar
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3. Divinsky, N., Rings and radicals, University of Toronto Press (1965).Google Scholar
4. Hartley, B., Locally nilpotent ideals of a Lie algebra, Proc. Cambridge Philos. Soc. 63 (1967), 257-272.Google Scholar
5. Jacobson, N., Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ. 34, Providence (1969).Google Scholar
6. Slater, M., Structure of alternative rings, and applications, Notices Amer. Math. Soc. 17 (1970), 561.Google Scholar
7. Tsai, C., Levitzki radical for Jordan rings, Proc. Amer. Math. Soc. 24 (1970), 119-123.Google Scholar
8. Zhevlakov, , Solvability and nilpotence of Jordan rings, Algebra i Logika Sem. 5 (1966), 37-58.Google Scholar
9. Zwier, P., Prime ideals in a large class of nonassodative rings, Trans. Amer. Math. Soc. 158 (1971), 257-273.Google Scholar