A Survey of Modern Algebra

a₁ addition affine transformation algebraic integers algebraic numbers automorphism b₁ basis canonical form cardinal number Chap characteristic roots coefficients column commutative complex numbers contains coordinates COROLLARY cosets defined definition degree determined diagonal direct sum distributive law divisor elementary elements entries equation equivalent Euclidean EXERCISES factors field F finite formula function Galois group Gaussian integers given group G hence homomorphism ideal identity implies integral domain inverse irreducible irreducible polynomial isomorphic Lemma linear transformation linearly independent matrix minimal polynomial monic multiplication nomial non-singular non-zero normal subgroup one-one correspondence ordered field orthogonal permutation plane polynomial f(x positive integers postulates Proof properties Prove quadratic form rational numbers real numbers relatively prime ring root field root of unity row-equivalent satisfies scalar Show solution square subfield subset subspace symmetric Theorem 13 tion unique vector space y₁ zero