Topics in AlgebraWiley, 20 de juny 1975 - 388 pàgines New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout. |
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a₁ a₂ abelian group automorphism b₁ basis characteristic roots coefficients commutative ring complex numbers conjugate COROLLARY cyclic group defined DEFINITION degree division ring divisor element of F equation Euclidean ring Example extension of F field F field of rational finite group finite number finite-dimensional Galois group given group G group of order hence Hermitian homomorphism ideal integral domain invertible irreducible isomorphic kernel Lemma Let G linear transformation linearly independent M₁ mapping matrix minimal polynomial multiplication n₁ n₂ nilpotent normal in G normal subgroup number of elements one-to-one p-Sylow subgroup permutation positive integer prime number Problem Proof prove rational numbers real numbers result right cosets satisfies solvable space over F splitting field subfield subgroup of G subgroup of order subset subspace Suppose symmetric u₁ unit element V₁ v₂ vector space w₁ whence