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Dimensionally nilpotent Jordan algebras


Author: J. Marshall Osborn
Journal: Proc. Amer. Math. Soc. 116 (1992), 949-953
MSC: Primary 17C10; Secondary 17C30
DOI: https://doi.org/10.1090/S0002-9939-1992-1079706-5
MathSciNet review: 1079706
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Abstract: An algebra $ A$ of dimension $ n$ is called dimensionally nilpotent if it has a nilpotent derivation $ \partial $ with the property that $ {\partial ^{n - 1}} \ne 0$. Here we show that a dimensionally nilpotent Jordan algebra $ A$ over a perfect field of characteristic not 2 or 3 is either (i) nilpotent, or (ii) one-dimensional modulo its maximal nilpotent ideal. This result is also extended to noncommutative Jordan algebras.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1079706-5
Article copyright: © Copyright 1992 American Mathematical Society

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