  Dickson's commutative semifields are an important class of finite division
algebras. We generalise Dickson's construction of commutative division algebras
by doubling both finite field extensions and central simple algebras and not
restricting us to the classical setup where a cyclic field extension is taken.
The latter case yields algebras which are no longer commutative nor
associative. Conditions for when the algebras are division algebras are given
that canonically generalise the classical ones known up to now. We investigate
when we obtain non-isomorphic algebras and compute all the automorphisms,
including the structure of the automorphism group in some cases.
