University Algebra

a₁ abelian group algebraic automorphism b₁ binary operation c₁ called canonical form characteristic roots coefficients column commutative ring complex numbers Corollary cyclic group defined Definition denote diagonal matrix divisors e₁ elementary equations Euclidean domain Example exists G₁ Galois extension group G group of order Hence hermitian homomorphism inner product space integer integral domain inverse irreducible isomorphism Let F Let f(x Let G Let H Let K/F linear map linear transformation linearly independent minimum polynomial module multiplication nilpotent non-singular matrix non-zero normal in G normal subgroup orthogonal orthogonal matrix prime ideal Proof Proposition quadratic form quotient R-module rank respect root of f(x roots in F Show solvable space over F splitting field subgroup of G submodule subspace Sylow symmetric symmetric matrix T(v₁ T₁ Theorem unique unit element unitary matrix v₁ V₂ vector space w₁ x₁ zero