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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nil algebras satisfying an identity of degree three
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by Raymond Coughlin PDF
Proc. Amer. Math. Soc. 34 (1972), 63-66 Request permission

Abstract:

Let A be a nonassociative algebra over a field F with a function $g:A \times A \times A \to F$ such that $(xy)z = g(x,y,z)x(yz)$ for all x, y, and z in A. Algebras satisfying this identity have been studied by Michael Rich and the author. It is shown here that a finite-dimensional nil power-associative algebra satisfying the above identity is nilpotent.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 63-66
  • MSC: Primary 17A30
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0292902-7
  • MathSciNet review: 0292902