Dimensionally nilpotent Jordan algebras

Osborn, J. Marshall

doi:10.1090/S0002-9939-1992-1079706-5

Dimensionally nilpotent Jordan algebras
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Proc. Amer. Math. Soc. 116 (1992), 949-953 Request permission

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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