AlgebraAllied Publishers |
Contents
1 Set Theory | 1 |
2 Unique Factorization Theorem | 6 |
3 Congruence | 12 |
4 Chinese Remainder Theorem | 20 |
5 Complex Integers | 23 |
6 Real Numbers and padic Numbers | 33 |
Group theory | 47 |
2 The Transformation Groups on Sets | 55 |
3 Linear Transformation and Matrix | 181 |
4 Module and Module over P I D | 196 |
5 Jordan Canonical Form | 214 |
6 Characteristic Polynomial | 223 |
7 Inner Product and Bilinear form | 232 |
8 Spectral Theory | 243 |
Polynomials in One Variable and Field Theory | 252 |
2 Algebraic Extension | 257 |
3 Subgroups | 62 |
4 Normal Subgroups and Inner Automorphisms | 73 |
5 Automorphism Groups | 82 |
6 pGroups and Sylow Theorems | 85 |
7 JordanHölder Theorem | 89 |
8 Symmetric Group Sn | 96 |
Polynomials | 102 |
2 Polynomial Rings and Quotient Fields | 108 |
3 Unique Factorization Theorem for Polynomials | 114 |
4 Symmetric Polynomial Resultant and Discriminant | 130 |
5 Ideals | 144 |
Linear Algebra | 160 |
2 Basis and Dimension | 165 |
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Common terms and phrases
a₁ algebraic closure algebraic extension assume b₁ B₂ basis c₁ canonical map characteristic values claim coefficients commutative group complex integers conclude Corollary cyclic deg(f(x Discussion easy Example factor finite extension finite field FL(n following definition following equation following theorem follows from Theorem function fundamental sequence Galois extension Galois group group G group of order homomorphism ideal integer integral domain invertible irreducible elements irreducible polynomial isomorphism Jordan canonical form Let f(x Let G Let us consider Let us define linear transformation linearly independent set m₁ matrix form minimal polynomial module Noetherian non-zero normal series normal subgroup Note orbits permutation polynomial f(x positive integer prime decomposition prime number primitive polynomial Proof Prove quotient groups R-module r₁ real numbers rotation separable algebraic Show splitting field subgroup of G subset subspace Suppose surjective transformation group u₁ unique vector space w₁