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A Class of Almost Commutative Nilalgebras

Published online by Cambridge University Press:  20 November 2018

Hyo Chul Myung
Hyo Chul Myung*
Affiliation:
University of Northern Iowa, Cedar Falls, Iowa
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The purpose of this paper is to investigate a class of nonassociative nilalgebras which have absolute zero divisors. If a nilalgebra is nilpotent, it, of course, possesses an absolute zero divisor. For the nilpotence of nonassociative nilalgebras, the situation however becomes quite complicated even in the finite-dimensional case. For example, Gerstenhaber [3] has conjectured the nilpotence of commutative nilalgebras. While Gerstenhaber and Myung [4] prove that any commutative nilalgebra of dimension ≦ 4 in characteristic ≠ 2 is nilpotent, Suttles [9] discovered an example of a 5-dimensional commutative nilalgebra which is solvable but not nilpotent.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1192 - 1198
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Albert, A. A., Power-associative rings, Trans. Amer. Math. Soc. 64 (1948), 552–593.Google Scholar
2. Bourbaki, N., Groupes et algèbr es de Lie, Actualités Sci. Indust., no. 1285 (Herman, Paris, 1960).Google Scholar
3. Gerstenhaber, M., On nilalgebras and linear varieties of nilpotent matrices. II, Duke Math. J. 27 (1960), 21–31.Google Scholar
4. Gerstenhaber, M. and Myung, H. C., On commutative power-associative nilalgebras of low dimension, Proc. Amer. Math. Soc. (to appear).Google Scholar
5. Jacobson, N., Lie algebras, Interscience Tracts in Pure and Appl. Math. no. 10 (Interscience, New York, 1962).Google Scholar
6. Myung, H. C., Some classes of flexible Lie-admissible algebras, Trans. Amer. Math. Soc. 167 (1972), 79–88.Google Scholar
7. Oehmke, R. H., Commutative power-associative algebras of degree one, J. Algebra 14 (1970), 326–332.Google Scholar
8. Schafer, R. D., Noncommutative Jordan algebras of characteristic , Proc. Amer. Math. Soc. 6 (1955), 472–475.Google Scholar
9. Suttles, D., A counterexample to a conjecture of Albert, Notices Amer. Math. Soc. 19 (1972), A–566.Google Scholar