ABSTRACT
This chapter examines identities of alternative algebras over a field. In Theorem 1, it shows that for any constant a > 0 and any alternative PI-algebra A the growth of identities of A is asymptotically less n!an. The second result treats the identities of graded alternative algebras. The third main result, Theorem 3, shows that the matrix algebra over an alternative PI-algebra is a non-associative algebra with a non-trivial identity of a very specific form. The chapter also provides a preliminary result about the identities in alternative algebras.
