Abstract
We show that any central simple algebra of exponent p in prime characteristic p that is split by a p-extension of degree pn is Brauer equivalent to a tensor product of 2⋅pn−1−1 cyclic algebras of degree p. If p=2 and n⩾3, we improve this result by showing that such an algebra is Brauer equivalent to a tensor product of 5⋅2n−3−1 quaternion algebras. Furthermore, we provide new proofs for some bounds on the minimum number of cyclic algebras of degree p that is needed to represent Brauer classes of central simple algebras of exponent p in prime characteristic p, which have previously been obtained by different methods.
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