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Авторизация |
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Поиск по указателям |
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Kurosh A. — Higher Algebra |
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Предметный указатель |
Abel, N. H. 12 232
Abelian group 383 385
Abelian group, finite 406ff
Abelian group, finite, complete survey of 413
Abelian group, finite, fundamental theorem on 406
Abelian group, indecomposable 405
Abelian group, primary 407
Absolute value 113
Addition 261
Addition in a group 385
Addition matrix 99
Addition of classes 268
Additive groups 385
Additive notation 400
Adjoint of a matrix 94
Affine space 178
Affine transformations 214
al — Khowarizmi, Muhammad 12
Aleksandrov, P. S. 414
Algebra of complex number, fundamental Algebra, theorem of 143
Algebra of polynomials over an arbitrary field 276
Algebra, differential 11
Algebra, elementary 7
Algebra, higher 7 9
Algebra, homological 13
Algebra, linear 7 8 13 15 276
Algebra, of matrices 87ff
Algebra, of polynomials 8 9 13
Algebra, subject of 9
Algebra, tensor 9
Algebra, theorem of, alternative proof of 337ff
Algebra, theory of 13
Algebra, topological 11
Algebra, universal 11
Algebra, universal, theory of 13
Algebraic geometry 9 326
Algebraic numbers 349ff
Algebraic numbers, conjugate 350
Algebraic numbers, set of 350
Algebraic operation 261
Algebraic over a field (e.g. element) 279 305
Algebraic structures 9
Algebraic study, subject of 9
Algebraic systems 10
Algebraic systems, ordered, theory of 11
Algebraically dependent (of a system of elements) 305
Algebraically independent (of a system of elements) 305
Algebraization of mathematics 11
Algorithm, division 129 131
Algorithm, Euclid’s 133 136 241
Algorithm, of successive division 133
Alphabetical method 310
Alphabetical order of terms of a polynomial 310 311
Alternating group 387
Analysis, functional 9 10
Angle, polar 113
Angle, vectorial 113
Annihilate (e.g. polynomial annihilated by a linear transformation) 381
Approximate calculations, theory of 58
Approximation of roots 250ff
Argument of a complex number 114
Argument of a product of complex numbers 115
Argument of a quotient of complex numbers 116
Arrangement(s) 27ff; see Permutations
Arrangement, definition of 28
Arrangement, even 29
Arrangement, odd 29
Aryabhata 12
Associativity of addition 108
Associativity of matrix multiplication 96
Associativity of multiplication 109
Augmented matrix 21
Axiomatic definition 103
Axis of imaginaries 112
Axis of reals 112
Bcher. M. 414
Baer, Reinhold 414
Bases 182
Bases, orthogonal 207
Bases, orthonormal 204 208
Bases, relationships between 185
Basis see Bases
Bhascara 12
Binomial coeificient 121
Binomial theorem, Newton’s 120
Birkhoff, Garret 414
Brahmagupta 12
Budan — Fourier theorem 246 249
Canonical -matrix 356 357
Canonical homomorphism 398
Canonical quadratic form 164
Capelli see Kronecker-Capelli theorem
Cardan, J. 12
Cardan’s formula 227 229
Cartan, Henri 414
Categories, theory of 13
Cauchy, A. L. 13
Cayley numbers 111
Cayley — Hamilton theorem 380 381
Cayley, A. 13
Change-of-basis matrix 185 186
Characteristic determinants 78
Characteristic matrix 199
Characteristic of a field 270
Characteristic polynomial of a matrix 200
Characteristic roots 199ff 216
Characteristic zero 270
Characteristic, finite 271
Chebotarev, N.G. 14 414 415
Chevalley, Claude 415
Ching Chou-chan 12
Ch’ang Ts’ang 12
Ch’in Chiu-Shao 12
Circle, closed 150
Class(es), addition of 268
Class(es), multiplication of 268
Class(es), opposite 294
Class(es), product of 293 301
Class(es), sum of 293 300
Class(es), unit 294 301
Class(es), zero 294 300
Closed circle 150
Coefficient, binomial 121
Coefficient, leading 126
Cofactors 43ff
Collar, A.R. 414
Common divisor 133
Commutative field 302
Commutative group 383
Commutative ring 267
Commutativity of addition 108
Commutativity of multiplication 109
Complementary minors 43
Complex linear spaces 181 202 209
complex numbers 107 110 112ff
Complex numbers, raising to a power 120
Complex numbers, taking roots of 120 122 123
Complex numbers, taking the square root of 122
Complex plane 112
Component(s) of an element 400
Component(s), primary 407
Congruent modulo 268
Conjugate (the conjugate of ) 118
Conjugate complex numbers 118
Conjugate elements 395
Conjugate numbers 119
Consistent system of linear equations 16
Constructive definition 103
Continuous function 144
Continuous groups, theory of 11 13
| Correspondence, isomorphic 181
Coset, left 392
Countable set 352
Cramer, G. 12
Cramer’s Rule 24 53ff 56 57
Cramer’s rule, new derivation of 97
Criterion, Eisenstein 344 345
Cubic equations 226
Cubic equations, incomplete 226
Cubic equations, with real coefficients 228
Cubic form 306
Cubic polynomial 127
Cycle length 35
Cycle(s) 34
Cycle(s) of degree 35
Cycle(s) of degree , disjoint 35
Cyclic groups 390ff
Cyclic groups, finite 391
Cyclic groups, infinite 390 391
Cyclic groups, primary 405 407
Cyclic permutation 34
Cyclic subgroups 389
Cyclotomic polynomial 345
De Moivre’s Formula 120
Decomposability of a finite Abelian group 407
Decomposable quadratic forms 172
Decomposition 34
Decomposition, direct 400
Decomposition, into cycles 34
Decomposition, left 392
Decomposition, of a group 391ff 407
Decomposition, of polynomials 284
Decomposition, right 392
Decomposition, summands of 400
Decomposition, unique (of a proper rational fraction) 159
Decomposition, unique (of a proper rational fraction)example of 160
Decrement of a permutation 26
Dedekind, R. 13
Definiteness of a form, positive 177
Definition, axiomatic 103
Definition, constructive 103
Degree of a -matrix 365
Degree of a polynomial 303
Degree of a term 303
Denumerable set 352
Dependence of vectors, linear 62ff
Derivative of a polynomial 141
Derivative of a polynomial, second 141
Descartes, R. 12
Descartes’ Rule of Signs 247
Descartes’ theorem 247 249
Determinant(s) 23
Determinant, axiomatic construction of 103
Determinant, characteristic 78
Determinant, definition of 23
Determinant, evaluating 462
Determinant, expansion of 47
Determinant, multiplication theorem for 93
Determinant, of th order 36ff
Determinant, of a system 54
Determinant, of second and third order 22ff
Determinant, second-order 23
Determinant, skew-symmetric 42
Determinant, theory of 12
Determinant, third-order 25 37
Determinant, Vandermonde 49 329 336
Determinate system 16
Diagonal matrices 371
Diagonal, principal 16
Diagonalization of a matrix 203
Difference 261
Differential algebra 11
Differentiating a sum and a product, formulas for 142
Dimension of a space 185
Diophantos of Alexandria 12
Direct decomposition 400
Direct product 406
Direct sum 400 403
Discriminant 326 334
Discriminant of a quadratic equation 335
Discriminant of an equation 228
Disjoint cycles 35
Dividend (of a polynomial) 306
Divisibility of polynomials 131 —133 305
Divisible 131
Divisible, exactly 131
Division algorithm 129 131
Division in a field, uniqueness of 267
Divisor(s) 131
Divisor, common 133
Divisor, elementary (of a matrix) 376
Divisor, elementary (of a polynomial) 376
Divisor, greatest common 131 133
Divisor, greatest common, of integers 133
Divisor, greatest common, of polynomials 133 135 138
Divisor, normal 394 398
Divisor, of a polynomial 306
Divisor, of unity 285
Duncan, W.J. 414
d’Alembert, J.R. 12
d’Alembert’s lemma 147 149
Eigenvalues 199
Eigenvector 200
Eilenberg, S. 414
Eisenstein criterion 344 —345
Element, component of 400
Element, conjugate 395
Element, identity (of a group) 385
Element, inverse 179 384
Element, multiples of 389
Element, of a set 261
Element, of infinite order 389
Element, opposite 179
Element, power of 389
Element, prime (of a ring) 285
Element, unit 269 383 385
Element, zero 180 264
Elementary algebra 7
Elementary divisors a polynomial 376
Elementary divisors of a matrix 376
Elementary matrix 363
Elementary symmetric polynomials 313
Elementary transformations 74
Elementary transformations of a matrix 355
Elimination of unknown 326 331
Equalizing coefficients, method of 23
Equation(s), th-degree 232
Equation(s), cubic 226
Equation(s), cubic, incomplete 226
Equation(s), cubic, with real coefficients 228
Equation(s), general theory of 12
Equation(s), higher-degree 231
Equation(s), homogeneous linear see Systems of homogeneous linear equations
Equation(s), nonhomogeneous see System of nonhomogeneous equations
Equation(s), of second, third, fourth degree 225ff
Equation(s), quadratic 225
Equation(s), quartic 230
Equation(s), quintic 232
Equation(s), solvability of by radicals 12
Equation(s), systems of linear see Systems of linear equations
Equivalence of -matrices 355ff
Equivalence relation 356
Euclidean algorithm see Euclid’s algorithm
Euclidean space(s) 204
Euclidean space(s), -dimensional 204 205
Euclidean space(s), isomorphic 208
Euclidean space(s), isomorphism of 208ff
Euclid’s algorithm 133 136 241
Expansion of a determinant 47
Extensions 271ff
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