Lectures on Modern Higher Algebra: Galois theory. Notes by Albert A. Blank, New York university, summer 1947, Part 1 |
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1817 LIBRARIES 3-cycle a₁ algebraic automorphisms CHIGAN clearly coefficients congruence congruence relation Consequently Consider consists construct Corollary corresponding cosets cyclic group defined degree denote digits division E/F is normal elements of F example Exercise extension field F fixed factor group factorization into primes field E field F field of f(x finite number fixed field follows Furthermore G contains greatest common divisor ground field group G group of E/F group of order Hence identity invariant subgroup inverse irreducible equation irreducible factors irreducible polynomial isomorphic Lemma linear factors linearly independent mapping mod p(x n-th root non-zero obtain permutation polynomial f(x polynomial over F possible postulates primitive principal ideal ring Proof proved rational functions rational numbers real numbers relation ring roots of unity satisfies separable polynomial solution solvable splitting field symmetric group Theorem unique factorization UNIV write zero