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.References
- A. Adrian Albert, Structure of algebras, American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. Revised printing. MR 0123587
- Raymond Coughlin and Michael Rich, Associo-symmetric algebras, Trans. Amer. Math. Soc. 164 (1972), 443–451. MR 310025, DOI 10.1090/S0002-9947-1972-0310025-X
- Richard D. Schafer, An introduction to nonassociative algebras, Pure and Applied Mathematics, Vol. 22, Academic Press, New York-London, 1966. MR 0210757
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