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Identities of Non-Associative Algebras

Published online by Cambridge University Press:  20 November 2018

J. Marshall Osborn
J. Marshall Osborn*
Affiliation:
University of Wisconsin
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In the first part of this paper we define a partial ordering on the set of all homogeneous identities and find necessary and sufficient conditions that an identity does not imply any identity lower than it in the partial ordering (we call such an identity irreducible). Perhaps the most interesting property established for irreducible identities is that they are skew-symmetric in any two variables of the same odd degree and symmetric in any two variables of the same even degree. The results of the first section are applied to commutative algebras in the remainder of the paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 78 - 92
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Kosier, F. and Osborn, J. M., Nonassociative algebras of degree 3, Trans. Amer. Math. Soc, 110 (1964), 484–492.Google Scholar
2. Losey, N., Simple commutative non-associative algebras satisfying a polynomial identity of degree five, Ph.D. thesis, Univ. of Wisconsin (1963).Google Scholar
3. Osborn, J. M., An identity of degree four, to appear in Proc. Amer. Math. Soc.Google Scholar
4. Osborn, J. M., A generalization of power-associativity, to appear in Pacific J. Math.Google Scholar