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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
Section, conic      585 591
Self-adjoint      358 372
Self-adjoint transformation      358 367 372
Self-conjugate subgroup      77
Semidirect product      409 414
Semigroup      39
Semilattice      475
Semimodular lattice      482
Semimodular lattices      482
Semisimple algebra      335
Separable algebraic extension      456
Separable element      456
Separable polynomial      448 449-50
SEQUENCE      23
Sequence of modules      530
Sesquilinear form      370
Set of morphism      165
Sets      1
Shear      249
Short exact sequence      327 380 413
Short Five Lemma      327
Signature      348 584
Signature of form      348
Similar matrices      253 309
Similar matrix      253 309
Similarity group      363
Similarity group and transformation      363
Similarity transformation      363
Simple algebra      335
Simple extension      442
Simple group      409 430 435
Simply ordered set      470
Simply ordered sets      470
Simultaneous indeterminates      140
Skeletal categories      156
Skew symmetric tensor      558-60
Skew-symmetric bilinear form      341
Skew-symmetric form      296 341
Skew-symmetric function      296
Skew-symmetric matrix      342
Skew-symmetric tensor      558-60
Small categories      510
Small category      510
Solution of equation by radicals      437 465ff
Solution of quadratic equations      436
Solutions of systems of equations      219
Solvable group      429 467
Space of covariant vectors      525
Space(s)      193ff 286 564ff 586ff
span      194 577
Special linear group      304 435
Special orthogonal group      362
Spectral theorem      367
Spectrum      367
Split extension      413
Split short exact sequence      328
Splitting field      447
Square matrix      227 243
Square-free integer      187
Stabilizer      71
Standard inner product      352 357 369
Strictly triangular matrix      243
Subalgebra, Boolean      489
Subcategory, full      487
Subdomain      103
Subfield      106
Subfunctor      135 502
Subgroup by conjugation      70
Sublattice      476
Submodule      167 379
Submonoid      56
Subnormal series      430
Subnormal subgroup      430
Subrings      90
Subset      2
Subspaces      202 576 594
Subspaces of vector spaces      202
Substitution in polynomial      108
Successor function      15
Sum of ideal      96
Sum of modules      168
Sum of natural numbers      18
Sum of submodules      168 183
Summand, direct      183 204 382
Summation convention      525
Surjection      6
Sylow $p$-subgroup      422ff
Sylow subgroup      422-26
Sylow theorem      423 425
Sylow theorems      423 424 425
Sylvester’s law of inertia      348
symmetric      12
Symmetric algebra      547
Symmetric bilinear form      341
Symmetric form      341
Symmetric group      45 63 468
Symmetric matrix      342
Symmetric property      208
Symmetric relation      12
Systems of linear equation      219
Table multiplication      44
Table, multiplication      44
Tensor algebra      540
Tensor field      528
Tensor of given type      524ff
Tensor product      293 319ff 324
Tensor product of a map      324
Tensor product of free modules      322
Tensor product of graded algebra      539ff
Tensor product of graded modules      531
Tensor product of modules      324 522
Tensor product of morphism      324
Tensor product of morphisms      324
Tensor product space      526
Tensor product spaces      526
Tensor space      524ff
Tensor spaces      524ff
Terminal object      499
Termwise multiplication      46
Termwise operation for rings      91 161
Termwise scalar multiple      161
Termwise sum      161 205
Ternary operation      13
Ternary operations      13
Torsion coefficients      399
Torsion element      383
Torsion free module      399
Torsion free modules      399
Torsion module      325 383ff 389 397
Torsion modules      325 383ff 389 397
Torsion product      325
Torsion submodule      400
Trace      311 571 579 583 597
Trace of affine map      571
Trace of biaffine functionals      579
Trace of matrix      311
Trace of quadratic functionals      580
Transcendental element      440
Transform of unit vectors      224
Transformation      4 68 235 561ff
Transformation group      68ff
Transitive      71
Transitive relation      263
Transitivity of sets      71 470
Translation of axioms      336
Translation of submodule      171
Translation space(s)      565
Transpose matrix      230 239 298 316
Transpose of an interval      481
Transpose of an orthogonal matrix      362
Transposition      66 157
Triangle axiom      354
Triangle inequality      264
Triangular matrix      243
Trichotomy      12 29 263
Trilinear function      295 522
Triple product      335
Trivial $R$-modules      162
Trivial morphism      149
Trivial ring      85
Truncated algebra      537
Two-sided ideal      95
Two-sided inverse      7 303
Unary operation      13 38
Unary operations      13 38
Underlying set      141 143
Underlying set functor      143 501
Underlying sets      141 143 501
Unimodular matrix      304
union      3
Unique morphism of graded algebra      541
Unique prime factorization      118 392
Unique prime factorization theorem      118
Uniqueness of universal element      523
Uniqueness of universal elements      523
UNIT      13 86
Unit element      173
Unit of groups      43
Unit sphere      359
Unit vectors      173 224
Unital morphism of rings      88 262
Unitary equivalence      376
Unitary equivalent      376
Unitary group      373
Unitary groups      373
Unitary matrix      373 376
Unitary space      369ff
Unitary spaces      369ff
Unitary transformation      373
Unity, roots of      279
Universal arrow      135
Universal bilinear function      318-19 522
Universal bound      470
UNIVERSAL class      510
Universal commutative ring      312
Universal element      60 134ff 148-49 495 511ff 513
Universal element for functor      137 148-49
Universal element to ring      137
Universal embedding in groups      130-31
Universal epimorphism      129
Universal graded algebra      541
Universal projections of product      150
Universal property of tensor algebra      541
Universal quadrilinear function      523
Universal ring      130
Universal trilinear function      522 523
Universal upper bound      474
Universality      129
Universality of 1-$N$ (monoid)      129
Universality of 1-$Z$ (group)      129
Universality of tensor product      321 330 522
Universe of discourse      13
Upper bound      145 271 473
Upper central series      427
Value of function      4
Vector space      193ff
Vector spaces      193ff
Vector spaces of finite type      168 379
Vector subspaces      202
Vector(s)      161
Void sets      2
Weights      562 566
Well-ordered      22 264
Z-module      162
Zero      86
Zero divisors      99
Zero element      50
Zero morphism      165
Zero of polynomial      310
1 2 3 4 5
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