On nearly commutative nodal algebras in characteristic zero

Rich, Michael

doi:10.1090/S0002-9939-1970-0251101-3

On nearly commutative nodal algebras in characteristic zero

Author: Michael Rich
Journal: Proc. Amer. Math. Soc. 24 (1970), 563-565
MSC: Primary 17.60
DOI: https://doi.org/10.1090/S0002-9939-1970-0251101-3
MathSciNet review: 0251101
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Abstract: In this paper we consider algebras satisfying the identity (I) $x(xy) + (yx)x = 2(xy)x$ and show that there are no nodal algebras of this type over any field $F$ of characteristic zero. The proof is obtained by first showing that if $x$ is an element of a finite-dimensional algebra satisfying (I) over a field of characteristic zero then the operator $L(x) - R(x)$ is nilpotent.

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