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| Авторизация |
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| Herstein I.N. — Topics in algebra |
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| Предметный указатель |
Hardy 378
hermite 216 218
Hermitian adjoint 318 319 322 336 339 340
Hermitian linear transformation 336 341
Hermitian matrix 319 322 336
Hexagon, regular 232
Higher commutator subgroups 252 253
hilbert 216 377
Hom(U, V) 173
Homogeneous equations, linear 189 190
Homomorphism(s) 54 131
Homomorphism(s) of groups 54
Homomorphism(s) of modules 205
Homomorphism(s) of rings 131
Homomorphism(s) of vector-spaces 173
Homomorphism(s), kernel of 56 131
Hurwitz 216 356 373
Ideal(s) 133 134 137
Ideal(s), left 136
Ideal(s), maximal 138
Ideal(s), prime 167
Ideal(s), principal 144
Ideal(s), radical of 167
Ideal(s), right 136
Idempotent 268
Identity element 27 28
Identity mapping 11
Identity(ies), Lagrange's 373
Identity(ies), Newton's 249
Image 11
Image of set 12
Image, inverse 12 58
Independence, linear 177
Index of H in G 41
Index of nilpotence 268 294
Index set 5
Inequality, Bessel 200
Inequality, Schwartz 194
Inequality, triangle 199
Inertia, Sylvester's law of 352
Infinite set 17
Inner automorphism(s) 68
Inner automorphism(s), group of 68
Inner product 193
Inner product spaces 191 337
Integer(s) 18
Integer(s), algebraic 215
Integer(s), Gaussian 149
Integer(s), partition of 88
Integer(s), relatively prime 19
Integers modulo n 22 23
Integral domain 126
Integral domain, characteristic of 129 232 235 237
Integral Quaternions 371
Internal direct product 106
Internal direct sum 174 175
Intersection of sets 3 4
Invariant construction (or proof) 187 188
Invariant subspace 285 290
Invariants of finite Abelian group 111
Invariants of nilpotent linear transformation 296
Inverse element 28
Inverse image 12 58
Inverse of mapping 15
Invertible linear transformation 264
Irreducible elements 163
Irreducible module 206
Irreducible polynomial 156
Irreducible set of linear transformations 291
Isomorphic groups 58
Isomorphic rings 133
Isomorphic vector spaces 173
Isomorphism of groups 58
Isomorphism of modules 205
Isomorphism of rings 133
Isomorphism of vector spaces 173
Jacobson 355 367
Jacobson's lemma 316 320
Jacobson's theorem 367
Jordan block 301
Jordan canonical form 299 301 302
Kaplansky 259
Kernel of homomorphism 56 131
Lagrange 40 356 371
Lagrange's identity 373
Lagrange's theorem 40 375
Law(s) of inertia, Sylvester's 352
Law(s), associative 14 23 27 28 36
Law(s), cancellation 34
Law(s), commutative 23
Law(s), distributive 23 121
Law(s), Sylvester's 352
Least common multiple 23 149
Left coset 47
Left ideal 136
Left-division algorithm 373
Left-invertible 264
Lemma, Gauss' 160 163 164
Lemma, Jacobson's 316 320
Lemma, Schur's 206
Length 192 193
Lindemann 216
Linear algebra 260
linear combination 177
Linear equations, determinant of system of 330
Linear equations, rank of system of 190
Linear functional 187 200
Linear homogeneous equations 189 190
Linear independence 177
Linear span 177
Linear transformation(s) 26
Linear transformation(s), algebra of 261
Linear transformation(s), decomposable set of 291
Linear transformation(s), determinant of 329
Linear transformation(s), elementary divisors of 308 309 310
Linear transformation(s), Hermitian 336
Linear transformation(s), invariants of nilpotent 296
Linear transformation(s), invertible 264
Linear transformation(s), irreducible set of 291
Linear transformation(s), matrix of 274
Linear transformation(s), nilpotent 268 292 294
Linear transformation(s), nonnegative 345
Linear transformation(s), normal 342
Linear transformation(s), positive 345
Linear transformation(s), positive definite 345
Linear transformation(s), range of 266
Linear transformation(s), rank of 266
Linear transformation(s), regular 264
Linear transformation(s), ring of 261
Linear transformation(s), singular 264
Linear transformation(s), trace of 314
Linearly dependent vectors 177
Liouville 216
Little Fermat theorem 44 366
MacLane 25
Mapping(s) 10
Mapping(s), composition of 13
Mapping(s), equality of 13
Mapping(s), identity 11
Mapping(s), inverse of 15
Mapping(s), one-to-one 12
Mapping(s), onto 12
Mapping(s), product of 13
Mapping(s), restriction of 17
Mapping(s), set of all one-to-one 15
Matrix(ces) 273
Matrix(ces) of a linear transformation 274
Matrix(ces), column of 277
Matrix(ces), companion 307
Matrix(ces), determinant of 324
| Matrix(ces), diagonal 282 305
Matrix(ces), Hermitian 319 322 336
Matrix(ces), orthogonal 346
Matrix(ces), permutation 284
Matrix(ces), real symmetric 347
Matrix(ces), row of 277
Matrix(ces), scalar 279
Matrix(ces), skew-symmetric 317
Matrix(ces), theory of 260 273
Matrix(ces), trace of 313
Matrix(ces), transpose of 316
Matrix(ces), triangular 284 286
Matrix(ces), unit 279
Maximum ideal 138
McCoy 169
McKay 87 119
Minimal polynomial 211 264
Module(s) 201
Module(s), cyclic 202
Module(s), difference 202
Module(s), direct sum of 202
Module(s), finitely generated 202
Module(s), fundamental theorem on finitely generated 203
Module(s), homomorphism(s) of 205
Module(s), irreducible 206
Module(s), isomorphism of 205
Module(s), order of element in 206
Module(s), quotient 202
Module(s), rank of 203
Module(s), unital 201
Modulus 22
Monic polynomial 160
Motzkin 144 169
Multiple root 233
Multiple, least common 23 149
Multiplicative system 142
Multiplicity of a characteristic root 303
Multiplicity of a root 220
Mutually disjoint 5
n-variables, field of rational functions 241
n-variables, polynomials in 162
n-variables, ring of polynomials in 162
Newton's identities 249
Nilpotence, index of 268 294
Nilpotent group 117
Nilpotent linear transformation 268 292 294
Nilpotent linear transformation, invariants of 296
Niven 216 259
Non-abelian 28
Nonassociative ring 121
Nonnegative linear transformation 345
Nontrivial subgroups 38
Norm 193
Norm of quaternion 372
Normal extension(s) 244—248
Normal linear transformation 342
Normal subgroup(s) 49
normalizer 47 84 99 361
nth root of unity, primitive 249
Null set 2
Number(s), algebraic 214—216
Number(s), constructible 228—230
Number(s), prime 19
Number(s), transcendental 214
Odd permutation 78 79
One-to-one correspondence 15
One-to-one mapping(s) 12
One-to-one mapping(s), set of all 15
Onto mappings 12
Operation, closure under 27
Order of a group 28
Order of an element 43
Order of an element in a module 206
Orthogonal complement 195
orthogonal matrices 346
Orthogonalization process, Gram — Schmidt 196
Orthonormal basis 196 338
Orthonormal set 196
Outer automorphism 70
Outer automorphism, group of 70
p-Sylow subgroup 93
Pappus' theorem 361
Partitions of an integer 88
Pentagon, regular 232
Perfect field 236
Period of an element 43
Permutation, even 78 79
Permutation, groups 75
Permutation, matrices 284
Permutation, odd 78 79
Permutation, representation 81
Permutation, representation, second 81
Perpendicularity 191 195
phi-function, Euler 43 71 227 250
Pigeonhole Principle 127
Pollard 259
Polynomial(s) in n-variables 162
Polynomial(s) over rational field 159
Polynomial(s) over ring 161
Polynomial(s), characteristic 308 332
Polynomial(s), content of 159 163
Polynomial(s), cyclotomic 250 362
Polynomial(s), degree of 152 162
Polynomial(s), division algorithm for 155
Polynomial(s), irreducible 156
Polynomial(s), minimal 211 264
Polynomial(s), monic 160
Polynomial(s), primitive 159 163
Polynomial(s), ring of 161
Polynomial(s), roots of 219
Polynomial(s), symmetric 243 244
Polynomial(s), value of 209
Positive linear transformation 345
Positive, definite 345
Prime element 146 163
Prime ideal 167
Prime number 19
Prime, primitive root of 360
Prime, relatively 19 147
Primitive nth root of unity 249
Primitive polynomial 159 163
Primitive root of a prime 360
Product of mappings 13
Product, cartesian 5 6
Product, direct 103
Product, dot 192
Product, inner 193
Projection 11
Proper subset 2
Quadratic forms, real 350
Quadratic residue 116 360
Quaternions 81 124 371
Quaternions, adjoint of 372
Quaternions, group of quaternion units 81
Quaternions, integral 371
Quaternions, norm of 372
Quotient group 52
Quotient module 202
Quotient ring 133
Quotient space 174
Quotient structure 51
Quotients, field of 140
R-module 201
R-module, unital 201
Radical of an ideal 167
Radicals, solvable by 250—256
Range of linear transformation 266
Rank of linear transformation 266
Rank of module 203
Rank of system of linear equations 190
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