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Mac Lane S., Birkhoff G.D. — Algebra
Mac Lane S., Birkhoff G.D. — Algebra



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Название: Algebra

Авторы: Mac Lane S., Birkhoff G.D.

Аннотация:

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance.
This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach — emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s — was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3 edition

Год издания: 1999

Количество страниц: 626

Добавлена в каталог: 10.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Hermitian bilinear form      376
Hermitian bilinear form(s)      376
Hermitian conjugate      372
Hermitian inner product      360
Hermitian matrix      373 376
Holomorph of a group      414
Hom      132 133 165
Hom set      132 496
Homogeneous linear equation      211 219
Homogeneous linear equations      211
Homogeneous morphism      163
Homogeneous morphisms      163
Homogeneous polynomial      338 536
Homogeneous polynomials      338 536
Homogeneous quadratic polynomials      345
Homogeneous systems of linear equations      219
Homogenous coordinates      596
Homomorphism      38
Hypersurfaces, quadric      591
Ideal in a graded algebra      537 538
Ideal of lattice      477
Ideal of lattices      477
Ideal(s)      95
Idempotent law      473
Identity      3 43
Identity arrow      496
Identity axiom for categories      496
Identity element      13 48
Identity function      5 141
Identity Law      6
Identity matrix      227 247 295
Identity morphism      227
Image      5 154 385 464
Image of function      5
Image of graded modules      531
Image of homomorphisms      464
Image of linear map      202
Image of morphism      75
Image of morphisms of groups      75
Image of subgroup      76
Image of subgroups      76
Image of sublattice      476
Image of sublattices      476
Image of submodule      169
Image of submodules      169
Implication      2
Improper divisors      111
Improper ideal      96
Improper ideals      96
inclusion      5 473
Inclusion diagram      143 472
Inclusion relation      324
Increasing list      560
Incursion relation      324
Independence      442 575
Indeterminates      106 137
Index of subgroup      73
Induction, mathematical      15 22
Inequality      20
Inertia, Sylvester’s law of      348
Infinite list      455
Infinite order      53
Infinite sets      159
Initial object      499
Injection      6
Injection of biproduct      178 179
Injection of coproduct      151
Injective function      6
Inner automorphisms      82 420
Inner product      294 304 351
Inner product space      338 352-54 355ff 529
insertion      137
Insertion function      5
Integers      23 25 27
Integral domain      99 113 120
Intermediate field      462
Internally graded algebra      538
Internally graded module      532
Internally modules, graded      532
Intersection      2 58
interval      476 480
Invariance of dimension      200 564
Invariant factors      385 387 391
Invariant factors of endomorphism      390
Invariant factors of matrix      391
Invariant function      254
Invariant of ideals      399
Invariant subgroup      77
Invariant subspace      389
Invariant subspaces      389
Invariant(s)      254
Inverse      7 43 48 303
Inverse function      7
Inverse image      76 154 476
Inverse matrix      246 304
Invertible      111
Invertible arrow      499
Invertible element      111
Invertible matrix      246 299 303
Invertible morphism      499
Invertible orthogonal matrix      362
Invertible real matrix      350
Irreducibility      268
Irreducible      9
Irreducible polynomial      112 267 275
Irreducible polynomials      112 267 275
Isomorphic factors      430
Isomorphic sets      39
Isomorphic sublattice      481
Isomorphism      38 135 523 595
Isomorphism of categories      501
Isomorphism of groups      43
Isomorphism of lattices      146
Isomorphism of posets      146
Isotone      474 481
Isotone mapping      481
Isotonic      21 263
Isotropy group      71
Iterated biproducts      183
Iterated function      15
Iterated tensor product      522ff 524
Jacobian matrix      527
Join in a lattice      145 473
Join in a poset      144
Join in lattices      145 473
Join irreducible      486
Join irreducible elements      486
Join of subring      91
Join-irreducible element      486
Join-irreducible point      489
Jordan - H$\ddot{o}$lder - Dedekind theorem      482
Jordan - H$\ddot{o}$lder theorem      430ff 431
Jordan canonical form      396
Jordan canonical form(s)      396
Jordan-form      396
Kernel      75 95 169 202 385
Kernel of morphism      75 95 169 537
Kernel of morphisms of graded algebra      537
Kernel of morphisms of groups      75
Kernel of morphisms of modules      169
Kernel of morphisms of rings      95
Kronecker delta      208 227 235 525
Lagrange interpolation formula      114
Lagrange theorem      73
Lagrange theorem on order      73
Laplace expansion      550
Lattice isomorphic map      480
Lattice of subset      477
Lattices      145 473
Lattices isomorphic map      480
Lattices of submodules      168
Law of Cosines      352
Leading coefficient      107
Leading coefficients      107
Least common multiple      118
Least element      41 264 470
Least member      264
Least upper bound      145 271 473
Left adjoint      517
Left and right adjoint functor      517 518
Left cancellation      48
Left coset      72
Left ideal      95
Left inverse      7 48
Left linearity      352 369 373
Left module      160 187
Left modules      160 187
Left multiplication      101
Left regular representation      69
Left translation      69
Left unit      13
Leibniz rule      454
Length in a poset      472
Length of a cycle      64
Length of a transposition      64
Length of a vector      351 353 370
Less than      263 470
LIMIT      269
Line      561 594
linear combination      194 224 552
Linear dependence      194
Linear equation      224 304 365 496 556
Linear equations      219 224 304 365 496 556 574
Linear field      455
Linear form(s)      207 239 296 339
Linear forms      207 239 296 339
Linear function      323
Linear independence      194 202 219 552
Linear map      163 202 203 226 232
Linear polynomial      107
Linear trace      583
Linear transformation      163 195 196 207 224 313 365 496 556
LIST      23 200
List of columns matrix      224
List of scalars      194
List of vectors      174 194
localization      127
Lower bound      144 271 473
Magnitude      117
Main theorem on quotient groups      80 410-11
Main theorem on quotient modules      172 211
Main theorem on quotient rings      97
Main theorem on tensor product      321
Map, rigid      588
Mapping diagram      5
Mapping function      501
Mathematical induction      15 22
Matrices of integers      403
Matrix function      213
Matrix of a composite      240ff
Matrix of a map      236 240 372 409
Matrix of a quadratic form      344
Matrix of a vector      238
Matrix of bilinear forms      338
Matrix of coefficients      339
Matrix of form      338
Matrix of hermitian form      376
Matrix of integers      403
Matrix of quadratic form      344
Matrix of quadratic forms      344
Matrix of vectors      238
Matrix product      225ff 339-40
Matrix relative to bases      223 340
Matrix(-ices)      23 223ff 388ff 400ff
Maximal element      471
Maximal ideal      125
Maximal join-irreducible      486
Meet      142 272 473
Meet in lattices      145 473
Meet semilattice      475
Member      2
Metacyclic group      415
Metric space      286 354 587
Metric space(s)      587
Minimal annihilates      383 389
Minimal annihilator      383 389
Minimal element      471
Minimal polynomial      312ff 389
Minimal polynomial of matrix      313
Minimum property      276 440
Minor      302 549
Mixed tensor      526
Modular identity      479
Modular inequality      474
Modular lattice      479
Modular lattices      479
Module isomorphism      183
Module(s)      160ff
Modules isomorphism      183
Modules, graded      530ff 534 540
Modulo $n$, congruence      32
Monic      107
Monic arrow      499
Monic morphism      499
Monic polynomial      107 268 312 390 469
Monoids      39
Monomorphisms      38 201 262 327 498
Monotonic function      498
Morphism of addition      37
Morphism of algebras      334
Morphism of binary operations      37
Morphism of Boolean algebras      488
Morphism of categories      141 229 501
Morphism of fields      100
Morphism of functor      507
Morphism of functors      507
Morphism of graded algebras      542
Morphism of graded modules      545
Morphism of groups      43
Morphism of lattices      145 146 476 481
Morphism of modules, graded      530
Morphism of monoids      41
Morphism of partial order      146
Morphism of posets      146
Morphism of rings      87 262
Morphism of S-pointed objects      513
Morphism of unitary spaces      373
Morphism(s)      37ff
Morphisms of group      43
Morphisms of modules      163
Motion, rigid      588
Multilinear form      295
Multilinear function      295 296 522ff
Multiplication by composition      166
Multiplication constant      336
Multiplication constants      336
Multiplication in rings      86ff
Multiplication of matrices      225
Multiplication of matrix      225
Multiplication of natural numbers      18
Multiplicative group      43
Multiplicative monoids      40
Multiplicity of eigenvalues      365
Multiplicity of roots      280 449
Mutiplicative group      43 452
Mutiplicative monoid      40
Mutiplicative unit      40
Natural $p$-adic      287 290
Natural bijection      513
Natural equivalence      507
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