Conference abstracts

Session S05 - Rings and Algebras

July 29, 18:30 ~ 18:55

## Identities of finitely generated alternative and Malcev algebras

### Ivan Shestakov

### University of São Paulo , Brazil - shestak@ime.usp.br

We prove that for every natural number $n$ there exists a natural number $f(n)$ such that every multilinear skew-symmetric polynomial on $f(n)$ variables which vanishes in the free associative algebra vanishes as well in any $n$-generated alternative algebra over a field of characteristic $0$. Similarly, for any $n$ there exists $g(n)$ such that every multilinear skew-symmetric polynomial on $g(n)$ variables vanishes in any $n$-generated Malcev algebra over a field of characteristic $0$. Before a similar result was known only for a series of skew-symmetric polynomials of special type on $2m+1$ variables constructed by the author, where $m>\tfrac{C^1_n+C^2_n+C^3_n}{2}$.