Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On nearly commutative nodal algebras in characteristic zero

Author: Michael Rich
Journal: Proc. Amer. Math. Soc. 24 (1970), 563-565
MSC: Primary 17.60
MathSciNet review: 0251101
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17.60

Retrieve articles in all journals with MSC: 17.60

Additional Information

Keywords: Nodal algebra, power-associative, characteristic zero, nilpotent, finite-dimensional
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society