Central simple algebras

Wedderburn’s factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z₂⊕Z₂⊕Z₂). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction of a maximal subfield which is a Galois extension of the center, with Galois group Z₂⊕Z₂. Use is made of the generic division algebras, with and without involution. This work was supported by the Israel Committee for Basic Research and the Anshel Pfeffer Chair.