Abstract Algebra: An Introduction |
Contents
Congruence in Z and Modular Arithmetic | 24 |
CHAPTER 6 | 40 |
Rings | 41 |
Copyright | |
18 other sections not shown
Common terms and phrases
a e G a₁ abelian group addition and multiplication additive group algebraic arithmetic Axiom bijective coefficients commutative ring complex numbers congruence class contains Corollary cosets cyclic group cyclic subgroup defined definition deg g(x denoted element of G equation Euclidean domain Exercise extension field finite abelian group finite group G₁ G₂ Galois greatest common divisor group G group of order Hence Hint homomorphism identity element integral domain inverse irreducible in Q[x isomorphic kernel Lagrange's Theorem Lemma Let F Let G multiplicative group N₁ nonempty nonzero element normal subgroup notation permutation positive integer principal ideal product of irreducibles proof of Theorem properties prove that G quotient group quotient ring r₁ real numbers ring with identity Section Show solution splitting field subgroup of G subgroup of order subring subset surjective Sylow p-subgroup Sylow Theorem unique factorization unit verify Z₂