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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

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