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Generalized Quaternion Algebras
Centrally Finite Division Algebras
Skew Polynomials and Division Rings
10 other sections not shown
a,b e algebraic extension Artin assumed binomial extension c e F center F central simple algebra char F coefficients commutative field constructed COROLLARY crossed product cyclic algebra cyclic group defined denoted derivation dimension division algebra division ring divisors element a e elementwise fixed endomorphism equation exponent F-algebra F-linear factor set field F finite dimensional finite number follows Galois group Hence hypotheses identity preserving indeterminate inverse isomorphic K-vector space Laurent series LEMMA Math matrix maximal subfield minimal polynomial monic multiplication nilpotent nonassociative nonzero elements normal notation power series principal right ideal Proc PROOF quaternions quotient ring right 9-derivation right ideal domain right Ore quotient ring homomorphism satisfies semigroup separable extension skew field skew polynomial ring skew subfield subgroup subring Suppose tensor product Theorem totally ordered twisted polynomial ring unique vector zero