Nil algebras satisfying an identity of degree three
Author:
Raymond Coughlin
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- 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 https://doi.org/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
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17A30
Retrieve articles in all journals with MSC: 17A30
Additional Information
Keywords:
Power-associative,
nil algebra,
nilpotent algebra
Article copyright:
© Copyright 1972
American Mathematical Society
