A Survey of Modern Algebra

a₁ affine transformation algebraic integer algebraic numbers automorphism b₁ Boolean canonical form cardinal number Chap characteristic coefficients column commutative ring complex numbers congruence contains coordinates COROLLARY cosets defined definition degree denote determinant distributive law elements equation equivalent Euclidean EXERCISES extension factor field F Find finite formula functions Galois group Gaussian integers given group G hence homomorphism ideal identity implies integers modulo integral domain inverse irreducible irreducible polynomial isomorphic Lemma linear transformation linearly independent monic non-singular non-zero normal subgroup one-one correspondence ordered field permutation plane polynomial f(x positive integers postulates Proof properties Prove quadratic form quotient rational numbers real numbers result root field root of unity satisfies scalar Show solution square subfield subset subspace symmetric Theorem 14 tion unique upper bound variables vector space Vn(F y₁ zero