Abstract Algebra: Theory and Applications |
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a₁ abelian group Abstract Algebra automorphism b₁ Boolean algebra CALIFORNIA/SANTA CRUZ codeword commutative ring complex numbers compute contains Corollary cosets CRUZ The University cryptosystem cyclic group decoding degree denote divides encoded equation error Euclidean Example exists extension field extension of F field extension field F finite extension finite field finite group function Fundamental Theorem G₁ Galois group group G group of order H₁ H₂ hence homomorphism integral domain inverse irreducible polynomial isomorphic lattice Lemma Let F Let G Let p(x linear mathematics matrix minimal polynomial multiplication n-tuple nonzero element normal subgroup one-to-one permutation polynomial in F[x polynomial p(x positive integer PROOF Proposition Prove or disprove real numbers solution solvable splitting field subfield subgroup of G Suppose Sylow Sylow p-subgroup Sylow Theorem symmetry unique UNIVERSITY OF CALIFORNIA/SANTA vector space