  If K/F is a finite abelian Galois extension of global fields whose Galois
group has exponent t, we prove that there exists a short exact sequence that
has as a consequence that if t is square free, then Dec(K/F)=Br_{t}(K/F) which
we use to show that prime exponent division algebras over Henselian valued
fields with global residue fields are isomorphic to a tensor product of cyclic
algebras. Finally, we construct a counterexample to the result for higher
exponent division algebras.
