Mcdonald B.R. — Linear algebra over commutative rings :: Электронная библиотека попечительского совета мехмата МГУ

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Mcdonald B.R. — Linear algebra over commutative rings

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Название: Linear algebra over commutative rings

Автор: Mcdonald B.R.

Аннотация:

This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. Our desire was to provide both an introduction and a survey of matrix theory over commutative rings. Many results and folklore in this subject are known to experts; however, these results are not easily discovered by the beginner or a scholar with only a temporary curiosity.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1984

Количество страниц: 568

Добавлена в каталог: 23.05.2011

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

Предметный указатель

$\lambda$ -ring      459
Additive functor      154
Adjoint      25 405 445 446
Adjoint isomorphism      206
Affine group      60 65
Alternating multilinear morphism      367
Annihilator      208
Annulet      208
Automorphism problem      75
Azumaya algebra      237
Baer Galois theory      214
Basic open set      255
Basis      102
Bass pairing      184
Bass theorem      497
Bezout Domain      135 329
Bimodule      227
Binet — Cauchy theorem      20 400 405
Cancellation property      147
Cayley — Hamilton theorem      31
Center of matrix ring      9
Characteristic ideal      31
Characteristic polynomial      31 414 440
Characteristic sequence      352 413
Characteristic value      324
Characteristic vector      324
Closed submodule      207
Cokernel      98
Column index      7
Column size      7
Commutator      46
Commutator subgroup      46
Companion matrix      64 416
Completable vector      311
COMPLEX      491
Compound matrix      28
Congruence transformation      58
Connected space      255
Correspondence theorem      99
Cramer's method      80
Cross product      239
D-ring      145
Dense subring      203
Derivation      30 237 365
Determinant      19 399 436
Determinant ideal      25 80
Determinant-trace polynomial      417 430
Dimension of free module      108
Dimensional ring      108
Direct sum of modules      99
Division algorithm      2
Dual basis      161
Dual basis of a projective module      130
Dual module      104
Elementary congruence subgroup      74
Elementary dilation      17 46
Elementary divisor ring      145 335
Elementary divisors      64
Elementary matrix unit      9
Elementary permutation      17
Elementary skew permutation      17
Elementary transvection      17 44
Endomorphism of finite rank      204
Entwining group      146
Enveloping algebra      229
Equivalence class      58
Equivalence transformation      58 135 242
Equivalent categories      156
Equivalent functors      156
Equivalent matrices      135
Exact sequence of modules      100
Exponential-trace formula      419 434
Extended module      352
Exterior algebra      366
Exterior rank      371
Factor Theorem      2
Faithful functor      159
Finite dimension      109
Finite free presentation      151
Fitting equivalent matrices      140
Fitting invariant      278
Fitting's lemma      288
Five lemma      100
Fraction functor      257
Free module      102
Free presentation      150 277
Frobenius normal form      65
Full functor      159
Functor (cofunctor)      154
Fundamental invariants      40
Fundamental theorem of projective geometry      119
Gabel's lemma      308
Galois correspondence      212
General congruence subgroup      74
General linear group      10 44
Generalized Bezout theorem      34
Generalized equivalence transformation      247
Generalized Nakayama lemma      272
Generalized Whitehead lemma      316
Generator      181
Generators of module      99
Ghost component      479
Grade      504
Harmonic quadruple      127
Hereditary ring      134
Hermite normal form      145
Hermite ring      335
Higman's linearization      71
Hilbert basis theorem      6
Ideal annihilator      36
Ideal class group      245
Ideal divisor      37
Ideal of relations      2 36
Ideal quotient      36
Indecomposable module      351
Inner automorphism      57
Inner derivation      239
Interior product      404
Intersection of submodules      99
Invariant factors      63
Invertible matrix      10
Invertible submodule      234 243
Jacobson radical      5
Kernel      98

Koszul complex      494 498
Krull — Schmidt property      350
Laurent polynomial      265
Left association      57
Left conjugation      57
Left exact functor      155
Local-global principal      124 339
localization      259
Matrix      7
Matrix addition      8
Matrix equality      7
Matrix multiplication      8
Matrix representation      107
Maximal spectrum      252
McCoy rank (matrix)      82
McCoy rank (module)      87
Minor      20
Modified Cayley — Hamilton theorem      274
Morita equivalent rings      202
Morphism      98
Multilinear alternating map      20
Nakayama's lemma      272
Newton identities      43
Nil radical      5
Noetherian reduction      24
Noetherian ring      5
Normal subgroup problem      74
Nullity of submodule      208
One in the stable range      53
Orientable module      390
Orthogonal complement      207
Outer product ring      397
Picard group      226 302
Presentation matrix      151
Prime spectrum      252
Primitive polynomial      54
Principal of irrelevance of algebraic inequalities      7 38
Progenerator (faithfully projective)      195
Projective cover      221
Projective module      105 128
Projective plane      126
Projective space      117
Projectively trivial ring      328
Projectivity      117 212
Pseudosimilarity      149
Pure vector      391
Quotient module      98
R-sequence      494
Radical of ideal      37
Radical of module      215
Radical of ring      216
Rank function      291
Rank of a free module      108
Rank of a matrix      82
Rank of a module      87
Rank one projective module      225 301
Rational normal form      65
Regular ring      255
Relation module      277
Remainder theorem      2
Residual rank      371
Resultant      40
Right division algorithm      33
Ring with many units      336
Row index      7
Scalar product      8
Schanuel's lemma      280
Schur's formulas      30
Semi linear morphism      115
Semi local ring      294
Semidirect product      59
Separability idempotent      236
Separable algebra      236
Serre's Conjecture      323
Serre's theorem      358
Short Five Lemma      101
Similarity class      57
Similarity transformation      57
Skew-symmetric matrix      12
Smith normal form      63
Special linear group      26 44
Split exact sequence      100
Splitting algebra      302
Stabilizer      58
Stable general linear group      46
Stable matrix      503
Stable ring      53
Stably free projective      307
Standard antiautomorphism      12
Standard automorphism      12
Standard characterizations of a projective module      129
Standard normal subgroup      74
Steinitz ring      106
Structure idempotents      292
Submodule      98
Substitution morphism      1
Substitution property      147
Sum of submodules      99
Support of a module      271
Swan's Lemma      354
Swan's Theorem      355
Sylvester's determinant identity      29
Symmetric algebra      374
Symmetric matrix      12
Symmetric multilinear morphism      376
Tensor (Kronecker) product of matrices      143
Tensor algebra      361
Towber ring      397
Trace      14 407 426
Trace ideal      185
Transformation group      56
TRANSPOSE      10
Ultrafunctor      306
Unimodular element      104
Unimodular row      48 55
Universal polynomial      462
Van Staudt's theorem      127
von Neumann regular ring      135
Weak exterior algebra      372
Whitehead determinant      70
Whitehead group      70 485
Whitehead's Lemma      69 141
Witt ring      479
Zariski topology      252

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