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## About associator nilpotence of finitely generated alternative algebras of characteristic 2 or 3. (English)

Authors: N.I. Sandu

### Abstract

It is proved that the free algebra of the variety of alternative commutative algebras (respectively, over a ring of characteristic 3) $\frak M$ with $n$ ($n \geq 2$) free generators is associator nilpotent of index $n - 1$ and associator solvable of index $\text{min}\{k \vert 3^k \geq 2n - 1\}$. Hence it follows that basis rank of variety $\frak M$ is infinite.

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