Abstract
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.
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