A Nonzero Element of Degree 7 in the Center of the Free Alternative Algebra

Abstract

We present a nonzero element of degree 7 in the center of the free alternative algebra over a field of characteristic 0 or greater than 7. This element is

This element is Malcev admissible and for the corresponding element w in a free Malcev algebra M of characteristic 0 or greater than 7, one gets that w M = 0.

Key Words:

• Alternative algebras
• Malcev algebras
• Center

Acknowledgments

The first version of this paper was completed in the beginning of 2000. At that time we were not aware of the result of Filippov (1999). We thank Professor I. P. Shestakov for bringing our attention to Filippov's result and for making many suggestions that improved the presentability of this paper.

This paper was written while the second named author held a grant from CNPq of Brazil. Part of the research was done when this author was visiting Iowa State University on a grant from FAPESP.