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Brown W.C. — Matrices over communicative rings
Brown W.C. — Matrices over communicative rings



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Название: Matrices over communicative rings

Автор: Brown W.C.

Язык: en

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 294

Добавлена в каталог: 26.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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