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| Herstein I.N. — Topics in algebra |
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| Предметный указатель |
 rational matrices, ring of 123
 matrix(ces) over F 278
matrix(ces) over F, algebra of all 278 279
(i, j) entry 277
15—gon, regular 232
17—gon, regular 232
9—gon, regular 232
Abel 237 252 256
Abelian group 28
Abelian group, structure of finite 109 204
Abelian group, structure of finitely generated 203
Adjoint(s) 318 321
Adjoint(s), Hermitian 318 319 322 336 339 340
Adjoint(s), quaternions 372
Adjunction of element to a field 210
Albert 356 377
Algebra 262
Algebra of all matrices over F 278 279
Algebra of linear transformations 261
Algebra, algebraic division 368
Algebra, boolean 9 130
Algebra, fundamental theorem of 337
Algebra, linear 260
Algebraic division algebra 368
Algebraic element 209 210
Algebraic extension 213
Algebraic integer 215
Algebraic number(s) 214—216
Algebraic of degree n 212 213
Algorithm, division 155
Algorithm, Euclidean 18
Algorithm, left-division 373
Alperin 119
Alternating group 80 256
Angle, trisecting 230
Annihilator of a subspace 188
Artin 237 259 378
Associates 146 162
Associative law(s) 14 23 27 36
Associative ring 121
Automorphism(s) of a cyclic group 66 67
Automorphism(s) of K relative to F 239
Automorphism(s) of the field 237
Automorphism(s), fixed field of a group of 238
Automorphism(s), group of inner 68
Automorphism(s), group of outer 70
Automorphism(s), inner 68
Axiom of Choice 138 367
Basis(es) 177 180
Basis(es), dual 187
Basis(es), orthonormal 196 338
Bessel inequality 200
Binary relation 11
Birkhoff 25
Birkhoff, G.D. 362
Boolean algebra 9 130
Boolean ring 130
Brauer — Cartan — Hua theorem 368
Burnside 119
Cancellation laws 34
Canonical form(s) 285
Canonical form(s), Jordan 299 301 302
Canonical form(s), rational 305 306 308
Cardan's formulas 251
Cartesian product 5 6
Cauchy 61 86 87
Cauchy's theorem 61 87
Cayley 71
Cayley — Hamilton theorem 263 309 334 335
Cayley's theorem 71 262
Center of a group 47 68
centralizer 47
Characteristic of integral domain 129 232 235 357
Characteristic polynomial 309 332
Characteristic root(s) 270 286—289
Characteristic root(s), multiplicity of 303
Characteristic subgroup 70
Characteristic vector 271
Characteristic zero 129 232 235
Choice, axiom of 138 367
Class equation 85 361
Class(es), congruence 22 353 354
Class(es), conjugate 83 89 361
Class(es), equivalence 7
Class(es), similarity 285
Closure under operation 27
Coefficients 153
Cofactor 334
Column of a matrix 277
Combination, linear 177
Commutative group 28
Commutative law 23
Commutative ring(s) 121
Commutative ring(s), polynomial rings over 161
Commutator 252
Commutator subgroup(s) 65 70 117 252 253
Companion matrix 307
Complement 5
Complement, orthogonal 195
Complex vector space 191
Composition of mappings 13
Congruence class 22 353 354
Congruence modulo a subgroup 39
Congruence modulo n 22
Congruent 352
Conjugacy 83
conjugate 83
Conjugate class(es) 83 89 361
Conjugate elements 83
Conjugate subgroups 99
Construction with straightedge and compass 228
Construction, invariant 187 188
Constructive 228 230
Constructive number 228
Content of polynomial 159 163
Correspondence, one-to-one 15
Coset, double 49 97 98
Coset, left 47
Coset, right 40
Cramer's rule 331
Criterion, Eisenstein 160 240 249
Criterion, Euler 360
Cube, duplicating of 231
Cycle decomposition 78
Cyclic group 30 38 49
Cyclic group, generator of 48
Cyclic module 202
Cyclic subgroup 38
Cyclic subspace 296 306
Cyclotomic polynomial 250 362
De Morgan rules 8
Decomposable set of linear transformations 291
Decomposition, cycle 78
Definite, positive 345
Degree n of an extension 208
Degree n of polynomial 154 162
Degree n, algebraic of 212 213
Degree n, alternating group of 80 256
Degree n, general polynomial of 251
Degree n, symmetric group of 28 75 241 253—257 284
Derivative 158 232 233
Desargues' theorem 361
Determinant 322
Determinant of linear transformation 329
Determinant of matrix 324
Determinant of system of linear equations 330
Diagonal matrix 282 305
Diagonal subset 6
Diagonalizable 305
Dickson 356
| Difference module 202
Difference set 5
Dihedral group 54 81
DIMENSION 181
Diophantos 356
Direct product of groups 103
Direct product of groups, external 104 105
Direct product of groups, internal 106
Direct sum of modules 202
Direct sum, external 175
Direct sum, internal 174 175
Disjoint sets 4
Disjoint sets, mutually 5
Distributive law(s) 23 121
Divisibility 144 145
Division algebra, algebraic 368
Division algorithm for polynomials 155
Division ring 126
Division ring, finite 360
Divisor(s) 18
Divisor(s), elementary 308 309 310
Divisor(s), greatest common 18 145
Domain, integral 126
Domain, unique factorization 163
Dot product 192
Double coset 49 97 98
Dual basis 187
Dual space 184 187
Dual, second 188
Duplicating the cube 231
Eigenvalue 270
Eisenstein criterion 160 240 249
Element(s), algebraic 209 210
Element(s), conjugate 83
Element(s), identity 27 28
Element(s), order of 43
Element(s), order of (in a module) 206
Element(s), period of 43
Element(s), prime 146 163
Element(s), separable 236
Elementary divisors of a linear transformation 308 309 310
Elementary symmetric functions 242 243
Empty set 2
Equality of mappings 13
Equality of sets 2
Equation(s), class 85 361
Equation(s), linear homogeneous 189 190
Equation(s), rank of system of linear 190
Equation(s), secular 332
Equivalence class 7
Equivalence relation 6
Euclidean algorithm 18
Euclidean rings 143 371
Euler 43 356 376
Euler criterion 360
Euler phi-function 43 71 227 250
Even permutation 78 79
Extension, algebraic 213
Extension, degree of 208
Extension, field 207
Extension, finite 208—212
Extension, normal 244—248
Extension, separable 236 237
Extension, simple 235 236
External direct product 104 105
External direct sum 175
Fermat 44 144 149 152 356 366 371
Fermat theorem 44 152 366
Fermat theorem, little 44 366
Field(s) 126 127 207
Field(s) of quotients 140
Field(s) of rational functions 162 241
Field(s) of rational functions in n-variables 241
Field(s) of symmetric rational functions 241
Field(s), adjunction of element to 210
Field(s), automorphism of 237
Field(s), extension 207
Field(s), finite 122 356
Field(s), perfect 236
Field(s), splitting 222—227 245
Finite abelian group(s) 109
Finite abelian group(s), fundamental theorem of 109 204
Finite abelian group(s), invariants of 111
Finite characteristic 129
Finite dimensional 178
Finite extension 208—212
Finite field 122 356
Finite group 28
Finitely generated abelian group 202
Finitely generated modules 202
Finitely generated modules, fundamental theorem on 203
Fixed field of group of automorphisms 238
Form(s), canonical 285
Form(s), Jordan canonical 299 301 302
Form(s), rational canonical 305—308
Form(s), real quadratic 350
Form(s), triangular 285
Four-square theorem 371
Frobenius 356 368 369
Frobenius theorem 369
Functional, linear 187 200
Functions, elementary symmetric 242 243
Functions, rational 162 241
Functions, symmetric rational 241
Fundamental theorem of algebra 337
Fundamental theorem of finite abelian groups 109 204
Fundamental theorem of finitely generated modules 203
Fundamental Theorem of Galois Theory 247
Galois 50 207
Galois group 237
Galois theory 237—259
Galois theory, fundamental theorem of 247
Gauss' lemma 160 163 164
Gaussian integers 149
Gelfond 216
General polynomial of degree n 251
Generator of cyclic group 48
Gram — Schmidt orthogonalization process 196
Greatest common divisor 18 145
Group(s) 28
Group(s) of automorphisms of K over F 239
Group(s) of automorphisms, fixed field of 238
Group(s) of inner automorphisms 68
Group(s) of outer automorphisms 70
Group(s), Abelian 28 109 203 204
Group(s), alternating 80 256
Group(s), automorphism(s) of 66 67
Group(s), center of 47 68
Group(s), commutative 28
Group(s), cyclic 30 38 49
Group(s), dihedral 54 81
Group(s), direct product of 103
Group(s), factor 52
Group(s), finite 28
Group(s), Galois 237
Group(s), generator of cyclic 48
Group(s), homomorphism(s) of 54
Group(s), isomorphic 58
Group(s), isomorphism(s) of 58
Group(s), nilpotent 117
Group(s), order of 28
Group(s), permutation 75
Group(s), quaternion units 81
Group(s), quotient 52
Group(s), simple 60
Group(s), solvable 116 252
Group(s), symmetric 28 75 241 253—257 284
Hall 119
Halmos 206 354
Hamilton 124 334 356
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