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| Авторизация |
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| Birkhoff G., Mac Lane S. — A Survey of Modern Algebra |
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| Предметный указатель |
Hilbert nullstellensatz 413
Holomorph of a group 313
Homogeneous coordinates 313
Homogeneous linear equations 51 190 219
Homogeneous quadratic forms 283
Homomorphism of a group 155
Homomorphism of a lattice 377
Homomorphism of a ring 69ff. 399
Hypercomplex numbers 396
Hyperplane 191
Ideal 80 400
Ideal quotient 410
Ideal, prime 405
Ideal, principal 80 402
Idempotent law 359
Identity 65
Identity element 2 133
Identity function 65
Identity Law 128 133
Identity matrix 185 225
Identity transformation 127
Image 33 241
Image of subspace 240
Imaginary component 108
Imaginary component numbers 107
Improper ideal 401
inclusion 357
Inclusion for Boolean algebra 365
Inclusion for partial ordering 372
Incomparable sets 358
Independence, affine 309
Independence, algebraic 73
Independence, linear 176
Indeterminate 63
Index of subgroup 146
Induction principle, finite 13
Induction principle, second 15
Inequality 10
Inequality of cardinal numbers 387
Inequality, Schwarz 201
Inequality, triangle 201
Infinite set 383
Inner automorphism 158
Inner product 198ff.
Inseparable polynomial 465
Insolvability of quintic 478
Integers, Algebraic 443
Integers, positive 9
Integral domain 3
Intersection 358
Intersection of ideals 407
Intersection of subgroups 145
Intersection of subspaces 174
Invariant subgroup 159
Invariant subspace 344
Invariants 277
Invariants of a matrix 334
Invariants of quadratic functions 287ff.
Inverse 38 47
Inverse law 133
Inverse of a matrix 229 235
Inverse of a transformation 128 136
Inverse, additive 173
Inverse, left, right 128
Invertible 16 76 229
Involution law 359
Involutory automorphism 232 235
Irrational number 95
Irreducible element polynomial 76 78ff.
Isometry 131
Isomorphism 35 65
Isomorphism of commutative rings 35
Isomorphism of groups 137
Isomorphism of lattices 377
Isomorphism of vector spaces 194 240
Iterated field extension 431ff.
Join 364
Join of ideals 408
Join of subgroups 146
Join-irreducible 378
Jordan Matrix 354
Kernel of homomorphism 156 207 400
Kronecker delta 275
Kronecker product 255
Lagrange interpolation formula 68
Lagrange interpolation formula, theorem for groups 146
Lattice 363 374ff.
Leading coefficient, term 66
Least common multiple 20 407
Least upper bound 96 374
Left coset 146
Left ideal 413
Left identity 134
Left inverse 128 134 238
Length of vector 199 201 301
Linear algebra 396
linear combination 173
Linear dependence 176
Linear equations 47 182
Linear form 280
Linear fractional substitution 315
Linear function 208
Linear groups 260ff. 268
Linear independence 176
Linear space see "Vector space"
Linear sum of subspaces 174
Linear transformations 216
Liouville number 439
Lorentz transformation 296
Lower bounds 96 374
Majorizable, cardinally 387
Matric polynomial ( -matrix) 340
Matrix 180ff. 214ff.
Matrix, circulant 340
Matrix, companion 338
Matrix, diagonal 228
Matrix, diagonally dominant 323
Matrix, hermitian 300ff.
Matrix, invertible 229
Matrix, Jordan 354
Matrix, monomial 228
Matrix, nilpotent 313
Matrix, nonsingular 229
Matrix, orthogonal 275
Matrix, reduced echelon 184
Matrix, row-reduced 183
Matrix, triangular 229
Matrix, unimodular 330
Matrix, unitary 300ff.
Maximal ideal 405
Maximum 291
Meet 363
Meet, irreducible 378
Metamathematics 373
Metric properties 202
midpoint 305
Minimal polynomial 337 423
Minimal polynomial, Boolean 370
Minimum 291
Minor of matrix 320
Modular lattice 376
Modulo, modulus (of a congruence) 25ff.
Monic polynomial 66
Monomial matrix 228
Multiple 16
Multiple, least common 20
Multiplication see also "Product"
Multiplication of matrices 222ff.
Multiplication table of group 135
Multiplication, scalar 170
| Multiplicity of roots 116
Natural multiple 415
Nilpotent matrix 313
Nonhomogeneous coordinates 313
Nonsingular linear transformation 235
Nonsingular matrix 229 237 246
Norm 257 281
Norm of complex number 439 448
Norm of vector see "Length of vector"
Normal field extension 468
Normal orthogonal basis 203ff.
Normal subgroup 159
Normal unitary basis 302
Null vector 172
Null-space, nullity 242
Odd permutation 153
One-one 33 128
Onto 33 128
Operation, binary 33
Operational calculus 226
Order of a group 146
Order of a group element 141
Order of a linear algebra 396
Order, isomorphism 59
Ordered domain 9 69
Ordered field 52
Orthogonal 176
Orthogonal group 275
Orthogonal matrix 275
Orthogonal projection 205
Orthogonal transformation 273
Orthogonal vector 119 302
Outer automorphism 158
Outer product of vectors 258
Paradox of Galileo 384
parallel 307
Parallelepiped 328
Parallelogram law 168
Partial fractions 90ff.
Partial order 371ff.
Partition 165
Peano postulates 57
Permutation 130 150
Permutation group 150
Permutation matrix 228
Polynomial 61ff.
Polynomial ideal 410ff.
Polynomial, form 63
Polynomial, function 65 411
Polynomial, inseparable 465
Polynomial, irreducible 76 78ff.
Polynomial, minimal 337 423
Polynomial, monic 66
Polynomial, separable 465
Polynomial, symmetric 154
Positive definite 289
Positive integers (postulates) 9 54
Positive semi-definite 297
Postulates 1
Power see also "Exponent"
Power of group element 140
Primary canonical form 353
Primary component 348
Prime 17
Prime field 419
Prime ideal 405
Prime integer 17
Prime, relatively 22 81
Primitive polynomial 85
Primitive root of unity 113
Principal axes 294 333
Principal axis theorem 294 303
Principal ideal 80 402
Principle of Finite Induction 13
Principle of Finite Induction, Second 15
PRODUCT see also "Multiplication"
Product of cardinal numbers 390
Product of cosets 161 166 404
Product of determinants 324
Product of ideals 409
Product of matrices 222 224
Product of transformations 127 222ff.
Product, tensor 251ff.
Projective conic 316
Projective geometry 312ff.
Projective group 314
Projective line 312ff.
Projective plane 312
Projective space 313
Projective subspace 313
Projective transformation 314
Proper homomorphism 401
Proper ideal 401
Proper subgroup 143
Properly contain 358
Quadratic equation 119
Quadratic form 283ff.
Quadratic function 296ff.
Quadratic integers 448
Quadric 296ff.
Quartic equation 121ff.
Quaternion group 258
Quaternions 255ff.
Quintic equation 478
Quotient 18 39 43
Quotient group 161ff.
Quotient ring 403ff.
Quotient space 206ff.
Quotients, field of 44
Radical of an ideal 413
Radicals, solution by 121
Range (of transformations) 33
Rank of bilinear form 282
Rank of matrix 185 241ff.
Rank of quadratic form 289
Rank, determinant 326
Rational canonical form 353
Rational form 63
Rational function 67 411
Rational integer 443
Rational number 42ff.
Real numbers 98
Real quadratic form 288ff. 335
Real symmetric matrix 290 294 335
Rectangular matrix 230
Recursive definition 14
Reducible polynomial 76
Reflection 124 216 273
Reflexive law 3 34
Reflexive law for divisibility 16
Reflexive law for equivalence relations 34 164
Reflexive law for inclusion 357
Reflexive law of congruence 26
Relations 34 163
Relations, binary 34
Relations, equivalence 34 164
Relatively prime 28 81
Remainder 18 74
Remainder theorem 75
Residue class 20 166 403
Residue class ring 403
Right coset 146
Right ideal 413
Right identity 128
Right inverse 134 238
Rigid motion 275
Ring 395
Ring of sets 378
Ring, commutative 1 29 69 402ff.
Ring, division 256 401
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