## AlgebraThis book is for the honors undergraduate or introductory graduate course. Linear algebra is tightly integrated into the text. |

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#### LibraryThing Review

User Review - rwturner - LibraryThingThis is a really fantastic introduction to algebra. The author asks a bit more of the reader than some other books at this level, but that's for the best. To paraphrase one of my professors, this is "the mathematician's introductory algebra textbook." Read full review

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### Common terms and phrases

abelian group algebraic arbitrary automorphism basis bijective called Chapter coefficients complex numbers compute conjugacy classes conjugate contains Corollary cosets cyclic group defined degree denote describe Determine diagonal dihedral group divides divisor domain dot product eigenvalues eigenvector element of G entries equation equivalent example field F finite group formula function Galois extension Galois group group G group of order hence hermitian homomorphism identity induction inverse irreducible polynomial isomorphic kernel lattice law of composition left multiplication Lemma Let F Let G linear combination linear operator linearly independent module n x n matrix nonzero normal subgroup notation obtained orbit orthogonal permutation plane polynomial ring positive definite prime integer principal ideal Proposition Prove quadratic quotient real numbers relation root rotation scalar Section solution splitting field square subfield subgroup of G subset subspace Suppose surjective Sylow symmetric group tion unitary variables vector space zero