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| Brown W.C. — Matrices over communicative rings |
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| Предметный указатель |
Addition of matrices 10
Adjoint 16
Algebra 81
Algebra, homomorphism 65 71 81
Algebraic closure 88
Algebraic curve 254
Annihilator 7 234 235
Antihomomorphism 235
Antirepresentation 235
Ascending chain condition 110
Associated primes 127
Associates 1
Basis 5
Bezout's theorem 253 259
Bilinear mapping 135
Canonical basis 6 78
Canonical forms, Frobenius normal form 200 211
Canonical forms, Hermite normal form 229
Canonical forms, Jordan 212
Canonical forms, rational 211
Canonical forms, real Jordan 213
Canonical forms, Smith normal form 189
Cayley — Hamilton theorem 70
Center of a ring 18
Characteristic value 214
Characteristic vector 214
Characteristic, ideal 71
Characteristic, polynomial 62
Chinese remainder theorem 175
Circle composition 24 239
Classical linear algebra 11
Classical matrix theory 11
Cofactor 15
Column partition 12
Column space 13
Comaximal ideals 176
Companion matrix 69
Complement 53
Complex field 27
Complex of R-modules 114
Complex right exact 114
Complex short exact 114
Conjugate, complex 27
Cramer's rule 43
Curve 254
Curve components 254
Curve order 255
Curve permissable position 256
Curve, reducible 254
Degree, of a poynomial 63 79
Determinant 14
Diagonal matrix 17
Diagonal reduction 180
Diagonalized 217
Dilation 26
DIMENSION 6 41
Diophantine equation 202
Direct sum 138 183
Discriminant 103
Division theorem 63
Divisor 66
Divisor, elementary 196
Domain, integral 2
Domain, PID 4
Domain, unique factorization 55
Eigenvalue 51 214
Eigenvector 214
Elementary divisor ring 184
Elementary divisors 196
Elementary transvections 26
Elimination theory 251
Empty set 3
Endomorphism ring 27
Equivalent matrices 184
Euclidean Domain 202
Exact complex 114
Extension of scalars 146
Factor 55
Factor, invariant 195
Faithful module 234
Field of fractions 40
Field, algebraically closed 88
Field, complex 27
Field, real 27
Finitely generated module 6
Finitely presented module 116
Fitting ideals 157
Formal degree 242
Formal leading coefficient 242
Formal power series 2 121
Free module 5
Frobenius normal form 200 211
Gaussian elimination 225
Gaussian integers 4
General linear group 16
Generalized matrix units 25
Generators of a module 6
Grade of an ideal 261
Group of units 1
Hamilton — Cayley theorem 70
Hermite normal form 229
Hermite ring 181
Hilbert basis theorem 4 111
Hilbert — Burch theorem 260 263
Hilbert, Nullstellensatz 252
Homogeneous polynomial 79
Homogeneous system of equations 36
Homogeneous transformation 255
Homomorphism 7
Homomorphism, image 7
Homomorphism, isomorphism 7
Homomorphism, kernel 7
Homomorphism, set of 7
Ideal, comaximal 176
Ideal, irreducible 125
Ideal, left, right 2
Ideal, maximal 54
Ideal, primary 123
Ideal, prime 52
Ideal, primitive 236
Ideal, principal 4
Ideal, quotient of 125
Idempotent 23
Identity matrix 16
Image 7
Imbedded prime 132
Indeterminates 78
Integral domain 2
Intersection multiplicity 258
Invariant factors 195
Irreducible polynomial 55
Irredundant primary decomposition 127
Isobaric polynomial 89
Isolated prime 132
Isomorphism 7
Jacobson radical 3
Jordan canonical form 212
Kernel of a homomorphism 7
Kronecker's method 244
Laplace expansion 15
Lattice of ideals 23
Leading coefficient 63
Left division 64
Left divisor 66
Left evaluation 65
| Left quasi-regular 239
Left remainder 64
Left zero divisor 1
linear combination 5
Linear group 16
Linearly independent 5
Local ring 118
localization 119 161
Matrix, addition of 10
Matrix, adjoint 16
Matrix, characteristic polynomial, of 62
Matrix, companion 69
Matrix, diagonal 17
Matrix, equivalent 184
Matrix, matrix units 11
Matrix, multiplication of 12
Matrix, relations 116
Matrix, set of 5
Matrix, similar 205
Matrix, trace of 18
Matrix, transpose 11
Matrix, zero 10
Maximal left ideal 3
Maximal prime belonging to 57
Maximal right ideal 3
Maximal with respect to S 53
Minimal polynomial 71
Minimal prime 55
Minor 14
Module 5 233
Module, direct summand 120 138
Module, faithful 234
Module, free 5
Module, homomorphism of 7
Module, irreducible 236
Module, projective 166
Module, torsion 163
Module, torsion-free 163
Monic polynomial 6
Monomial 6 78
Multilinear function 14
Multiplicative subset 52
Nakayama's lemma 118
Nil radical 54
Noetherian ring 4 123
Nontrivial solution 36
Null ideal 71
Null space 71
Pairwise comaximal ideals 176
Partially ordered set 3 230
Partitions of matrices 12
Peirce decomposition 23
Permissable position 256
Permutation, even 14
Permutation, matrix 26
Permutation, odd 14
Permutation, sgn 14
Polynomial, degree of 63 79
Polynomial, homogeneous 80
Polynomial, irreducible 55
Polynomial, isobaric 89
Polynomial, roots of 76
Polynomial, weight of 89
Presentation 116
Primary ideal 123
Prime 52
Prime, embedded 132
Prime, isolated 132
Primitive ideal 4 26
Principal ideal domain 4
Principal ideal ring 4 175
Product of matrices 12
Projective dimension 167 265
Projective module 166
Projective space 253
Proper ideal 3
Quasi-regular 4 239
Quaternions 27
Quotient ring 40
Radical of an ideal 54
Radical, Jacobson 3
Radical, nil 54
Rational normal form 211
Rationals 2
Real Jordan form 213
Regular element 1
Regular sequence 260
Relation 230
Relation, anti-symmetric 230
Relation, reflexive 230
Relation, transitive 230
Relations matrix 116
Representation 235
Representation, faithful 236
Representation, irreducible 236
Resultant 85
Resultant system 247
Right division 64
Right divisor 66
Right evaluation 65
Right exact sequence 114
Right quasi-regular 239
Right zero divisor 1
Ring, commutative 1
Ring, elementary divisor 184
Ring, Hermite 181
Ring, integral domain 2
Ring, Noetherian 4
Ring, primitive 236
Ring, principal ideal domain 4
Ring, principal ideal ring 4
Ring, simple 23
Roots of characteristic polynomial 216
Row partition 12
Row space 13
Scalar multiplication 10
Sequence, elementary divisors 196
Sequence, invariant factors 195
Sequence, regular 260
Short exact sequence 114
Similar matrices 205
Simple ring 23
Smith normal form 189
Snake lemma 262
Solution to linear system 35
Special linear group 19
Special PIR 176
Specialization 81
Spectrum 214
Sum of matrices 10
Sylvester's determinant 84
Sylvester's matrix 82
Tensor product 140
Torsion element 163
Torsion module 163
Trace of a matrix 18
Transpose of a column 6
Transpose of a matrix 11
Transvection 26
Universal mapping problem 137
Vandermonde matrix 103
Variables 6
Weight of a polynomial 89
Zero divisor 1 7
Zero matrix 10
Zero vector 35
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