A lower bound on the essential dimension of simple algebras

Let [math] be a prime integer and [math] a field of characteristic different from [math] . We prove that the essential [math] -dimension ed [math] of the class [math] of central simple algebras of degree [math] is at least [math] . The integer [math] measures complexity of the class of central simple algebras of degree [math] over field extensions of [math] .