Essential dimension of central simple algebras

Let p be a prime integer, 1≤s≤r be integers and F be a field of characteristic different from p. We find upper and lower bounds for the essential p-dimension ed _p (( Al{{g}_{{{{p}^r},{{p}^s}}}} )) of the class ( Al{{g}_{{{{p}^r},{{p}^s}}}} ) of central simple algebras of degree p ^r and exponent dividing p ^s . In particular, we show that ed(Alg _8,2)=ed₂(Alg _8,2)=8 and ed _p (( Al{{g}_{{{{p}^2},p}}} ))=p ²+p for p odd.