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Авторизация |
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Kurosh A. — Higher Algebra |
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Предметный указатель |
Factor groups 394 395 396
Factor groups, examples of 397
Factor, -fold 284
Factor, double 284
Factor, invariant 361
Factor, multiple 284 287
Factor, multiple, isolation of 288
Factor, simple 284
Factor, single 284
Factor, triple 284
Factorization of polynomials 284
Factorization of polynomials into irreducible factors 281
Faddeyev, D.K. 414
Faddeyeva, V.N. 414
False position, method of 251
Ferrari, L. 12 230
Ferro, S. del 42
Fibonacci, L. 12; see Leonardo of Pisa
Field(s) 9 267
Field, characteristic of 270
Field, commutative 302
Field, concept of 257
Field, definition of 267
Field, division in, uniqueness of 267
Field, finite 268
Field, general theory of 13
Field, number 257 259 271
Field, obtained by adjoining an element 272
Field, of algebraic functions, theory of 10 13
Field, of algebraic numbers, theory of 10 13
Field, of complex numbers, construction of 273 275 295
Field, of complex numbers, uniqueness of 272
Field, of rational fractions 297ff
Field, of rational numbers 260 341
Field, splitting 296
Finite abelian groups 406ff
Finite Abelian groups, fundamental theorem on 406
Finite characteristic 271
Finite cyclic group 391
Finite fields 268
Finite group 383
Finite rings 268
Finite-dimensional linear space 183
Finite-dimensional spaces 182
Finite-dimensional unitary spaces 210
Form, cubic 306
Form, Jordan normal 370
Form, Jordan normal, reduction of a matrix to 375
Form, linear 62 306
Form, negative definite 177
Form, normal 169 170
Form, normal, of a matrix 355ff
Form, of degree 306
Form, pairs of 219 223
Form, positive definite 174ff
Form, quadratic 306 (see also Quadratic form)
Form, quartic 306
Form, theory of 8
Form, trigonometric (of complex number) 114
Formula, Cardan’s 227 229
Formula, de Moivre’s 120
Formula, for differentiating a sum and a product 142
Formula, Lagrange interpolation 153
Formula, Newton’s 323
Formula, Taylor’s 145
Formula, Vieta’s 154 296 313
FOURIER see Budan — Fourier Theorem
Fraction, partial 157
Fraction, rational 156 298
Fraction, rational, field of 297ff
Fraction, rational, in lowest terms 156
Fraction, rational, proper 156
Fraction, rational, simplified 156
Fraction, rational, symmetric 321
Fraction, symmetric rational 321
Fractional rational functions 156
Frazer, R.A. 414
Free unknowns 79
Frobenius, F.G. 13
Function, continuous 144
Function, fractional rational 156
Function, rational integral 337
Function, symmetric 312
Functional analysis 9 10
Fundamental system of solutions 84
Fundamental theorem of higher algebra 143
Fundamental theorem of the algebra of complex numbers 143ff
Fundamental theorem of the algebra of complex numbers, alternative proof of 337
Fundamental theorem on finite Abelian groups 406
Fundamental theorem on symmetric polynomials 314 316 319
Fundamental theorem on the similarity of matrices 367
Fundamental theorem, corollaries to 151ff
Galois, E. 9 12 13 232
Galois, theory of 11 13
Gantmacher, F.R. 414
Gauss, C.F. 12 143
Gauss’ (or Gaussian) elimination process 21
Gauss’ (or Gaussian) lemma 307 342
Gauss’ (or Gaussian) method 17 18 20
Gelfand, I.M. 414
Generate (verb) (subgroup generated by subgroups) 401
Generation of a linear subspace 196
Generator 390
Geometry, algebraic 9 326
Geometry, projective 11
Graeffe method 256
Grassmann, H. 13
Grave, D.A. 13 415
Greatest common divisor 131 133
Greatest common divisor of integers 133
Greatest common divisor of polynomials 134 135 138
Group(s) 10 382ff
Group(s), Abelian 383 385
Group(s), Abelian, finite 406ff
Group(s), Abelian, indecomposable 405
Group(s), Abelian, primary 407
Group(s), addition in 385
Group(s), additive 385
Group(s), alternating 387
Group(s), commutative 383
Group(s), continuous 11 13
Group(s), continuous, theory of 13
Group(s), cyclic 390ff
Group(s), cyclic, primary 407
Group(s), decomposition of 391ff
Group(s), definition of 382 383
Group(s), factor 394 395 396
Group(s), factor, examples 397
Group(s), finite 383
Group(s), finite Abelian 406ff
Group(s), finite Abelian, complete survey of 413
Group(s), finite Abelian, fundamental theorem on 406
Group(s), finite cyclic 391
Group(s), finite cyclic, general theory of 13
Group(s), finite cyclic, infinite cyclic 390 391
Group(s), finite cyclic, isomorphic 385
Group(s), finite cyclic, Lie 11
Group(s), finite cyclic, multiplication in 382
Group(s), finite cyclic, multiplicative 386 391
Group(s), finite cyclic, noncommutative 387
Group(s), finite cyclic, order of 383
Group(s), finite cyclic, primary 407
Group(s), finite cyclic, primary Abelian 407
Group(s), finite cyclic, primary cyclic 405 407
Group(s), finite cyclic, theory of 10 382
Group(s), finite cyclic, theory of, Soviet school of 14
Gurevich, G.B. 414
Hlder, O. 13
Hamilton see Cayley-Hamilton theorem
Hamilton, W.R. 13
| Hecke, E. 415
Height of a polynomial 353
Higher algebra 7 8
Higher-degree equations 231
Highest term of a polynomial 311
Hisb al-jabr w’al-mug-balah 12
Hodge, W. V.D. 415
Homogeneous linear equations see Systems of homogeneous linear equations
Homogeneous polynomial 306
Homological algebra 13
Homomorphic mapping 397
Homomorphism(s) 394 397
Homomorphism(s), canonical 398
Homomorphism(s), theorem on 398
Horner method 140 141
Hurwitz, A. 13
Hypercomplex numbers, theory of 10
Hypercomplex systems, theory of 13
Ideals, theory of 10 13
Identity element of a group 383 385
Identity matrix 93
Identity permutation 31
Identity transformation 189 195 214
Image 188
Imaginaries, axis of 112
Imaginaries, pure 112
Imaginary part 112
Imaginary unit 112
Incomplete cubic equation 226
Inconsistent system of linear equations 16
IndecomposabiHty of groups 405
Indecomposable Abelian group 405
Indefinite quadratic forms 177
Indeterminate system 16
Index of a subgroup 393
Index of inertia, negative 172
Index of inertia, positive 172
Inertia, law of 169 170
Inertia, negative index of 172
Inertia, positive index of 172
Infinite cyclic group 390 391
Infinite-dimensional linear spaces 181
Infinite-dimensional spaces 9
Integers, system of 107
Integral rational functions 156
Interpolation formula, Lagrange 153
Interpolation, linear, method of 251
Invariant (adj.) 211
Invariant factors 361
Invariant subgroup 394
Invariants, theory of 9
Inverse (to a class) 301
Inverse element 179 384
Inverse linear transformation 199
Inverse matrices 93
Inverse matrix, left 94
Inverse matrix, right 94
Inverse of a permutation 33
Inverse operation 261
Inverse polynomial 129
Inverse transformation 199
inversion 29
Irrational numbers 107
Irreducible (of a polynomial) 281 306
Irreducible (of a solution) 230
Isomorphic (adj.) 272
Isomorphic correspondence 182
Isomorphic Euclidean spaces 208
Isomorphic groups 385
Isomorphic real linear spaces 181
Isomorphism(s) 178 181
Isomorphism(s) of Euclidean spaces 208
Isomorphism(s) of fields 272ff
Isomorphism(s) of rings 272ff
Iterative procedures 58
Jacobson, N. 414 415
Jordan matrices 370
Jordan matrix of order 370
Jordan normal form 370
Jordan normal form, reduction of a matrix to 375
Jordan submatrix 371
Jordan, M.E.C. 13
Kernel of a homomorphism 398
Kernel of a linear transformation 197
Khayyam, Omar 12
Kronecker — Capelli theorem 77 78 81
Kronecker, L. 13 345
Kummer, E.E. 13
Kurosh, A.G. 415
Lagrange interpolation formula 153
Lagrange, J.L. 12 13
Lagrange’s Theorem 393
Laplace, P. S. 12
Laplace’s theorem 50 51
Lattice 11
Lattice theory 11 13
Law of inertia 169 170
Leading coefficient 126
Left coset 392
Left decomposition 392
Left inverse matrix 94
Left-identity 384
Left-inverse 385
Lemma see Theorem
Lemma, d’Alembert’s 147 149
Lemma, Gauss’ (or Gaussian) 307 342
Lemma, on the increase of the modulus of a polynomial 146
Lemma, on the modulus of the highest-degree term 145
Leonardo of Pisa 12; see Fibonacci
Lie groups, theory of 11
Lie, S. 13
Linear algebra 7 8 13 15 276
Linear combination of vectors 62
Linear dependence of vectors 62ff
Linear equations see Systems of linear equations
Linear form 62 306
Linear interpolation, method of 251
Linear polynomials 127 139
Linear spaces 7 178ff
Linear spaces, -dimensional 185
Linear spaces, complex 202 209
Linear spaces, finite-dimensional 183
Linear spaces, infinite-dimensional 181
Linear subspaces 195ff 202
Linear subspaces, generation of 196
Linear substitution 87
Linear transformation(s) 87 89 188
Linear transformation(s), inverse 199
Linear transformation(s), kernel of 197
Linear transformation(s), nonsingular 93 198
Linear transformation(s), nonsingularity of 224
Linear transformation(s), null space of 197
Linear transformation(s), operations on 193
Linear transformation(s), product of 193
Linear transformation(s), product of, by a scalar 193
Linear transformation(s), rank of 197
Linear transformation(s), singular 93
Linear transformation(s), spectrum of 200
Linear transformation(s), with a simple spectrum 202
Linearly dependent system of vectors 63 64
Linearly independent system of vectors 63
Lobachevsky, method of 256
Lobachevsky, N.I. 13
Lyapin, E.S. 414 415
Maltsev, A.I. 414
Mapping, homomorphic 397
Matrices see also Matrix
Matrices, -matrices 355
Matrices, -matrices, canonical 356 357
Matrices, -matrices, equivalence 355ff
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