The Composition Structure of Alternative and Malcev Algebras

Abstract

We construct a polynomial of degree 5 from the associative nucleus (kernel) of the free alternative algebra. We show that this polynomial is of minimal degree. Using this polynomial, we obtain decompositions of the varieties of alternative and Malcev algebras.

Key Words:

• The varieties of alternative and Malcev algebras

2010 Mathematics Subject Classification:

• 17D05
• 17D10

ACKNOWLEDGMENTS

The author gratefully acknowledges to Professor Ivan Shestakov for suggesting the problem and for many helpful comments. The author wishes to express his gratitude to Dr. Jordan Dale Hill for many helpful suggestions during the preparation of the paper.

Notes

Communicated by I. Shestakov.