Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Birkhoff G., Mac Lane S. — A Survey of Modern Algebra
Birkhoff G., Mac Lane S. — A Survey of Modern Algebra



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: A Survey of Modern Algebra

Авторы: Birkhoff G., Mac Lane S.

Аннотация:

A new edition of the classic undergraduate text introducing abstract algebra using concrete examples. The authors ground their explanations with computational and theoretical exercises to develop the student's "power to think for himself," covering topics such as the role of careful proof in algebra, linear algebra as grounded in geometry, groups as expressions of symmetry, and subgroups and subsystems leading to lattice theory. This volume is a corrected version of the 4th edition and is offered by a new publisher


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Fourth Edition

Год издания: 1977

Количество страниц: 500

Добавлена в каталог: 04.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abelian group      133
Absolute value      10
Absolute value of complex number      110
Absorption law      362
Addition      see also "Sum"
Addition of cardinal numbers      390
Addition of complex numbers      107
Addition of inequalities      10
Addition of matrices      220ff.
Addition of polynomials      62ff.
Addition of vectors      170
Additive group      170 269 415 446
Additive inverse      2
Adjoint of matrix      325
Affine geometry      305ff.
Affine group      269
Affine independence      309
Affine space      305
Affine subspace      306
Affine transformation      270
algebraic      421
Algebraic extension      422
Algebraic function field      427
Algebraic integer      443
Algebraic number      435
Algebraic number field      438
Algebraic variety      410
Algebraically closed      437
Algebraically complete      437 454
Algebraically independent      73
Alias-alibi      271
Alternating group      154
Angle between vectors      202
Annihilator      211
Anti-automorphism      232
Anti-symmetric law      357 372
Archimedean property      99
Argument of complex number      110
Arithmetic, fundamental theorem of      23
Associate      76
Associative law      2
Associative law for groups      127 133
Associative law for matrices      224
Associative law for rings      2
Associative law for transformations      127
Associative law, general      13
atom      378
Augmented matrix      247
Automorphism      36
Automorphism of a group      157
Automorphism of a vector space      235
Automorphism, inner      158
Automorphism, involutory      232
Automorphism, outer      158
Axiom of Choice      129 384
Barycentric coordinates      310
Base of parallelepiped      328
Basis      176 193
Basis for ideals      402 411
Basis of vector spaces      176 193
Basis, change of      260
Basis, normal orthogonal      203ff.
Basis, normal unitary      302
Bijection      33 129
Bilinear form      281
Bilinear function      251
Bilinear multiplication      225
Bilinearity      199
Binary operation      33
Binary relation      34
Binomial coefficients      14
Block multiplication      234
Boolean algebra      359 361
Boolean algebra, free      377
Boolean algebra, isomorphism of      377
Boolean function      368
Boolean function polynomial      368
Boolean function, minimal polynomial      370
Bounds (lower, upper, etc.)      96
Cancellation law      3 391
Cancellation law for cardinal numbers      391
Cancellation law for groups      134
Canonical form      187 248 277
Canonical form for linear forms      281
Canonical form for matrices      187
Canonical form for quadratic forms      283ff.
Canonical form, bilinear      282
Canonical form, disjunctive      369
Canonical form, Jordan      355
Canonical form, primary rational      353
Canonical projection      207
Cantor's diagonal process      386 436
cardinal number      381 387
Cartesian product      34
Cayley — Hamilton theorem      340
Cayley's theorem      139 269 398 482
Center of a group      144
Centroids      308
Chain      376
Characteristic      415ff.
Characteristic equation      333
Characteristic polynomial      331ff.
Characteristic root      265 332
Characteristic vector      265 332
class      see "Set"
Closure under an operation      1
Codomain of transformation      33 241
Cofactor      319
Column equivalent      249
Column operation      248
Column rank      250
Column vector      232
Commutative group      133
Commutative law      2
Commutative law, general      14
Commutative ring      1 69
Commutator      163
Companion matrix      338
Complement in a lattice      375
Complementarity law      359
Complementary subspaces      196
Complementation      362
Complete ordered domain      98
Complete ordered field      98
Complete set of invariants      277
Completing the square      119
Complex number      41 107ff.
Complex plane      110
Composite      127
Congruence      25 43 see
Congruence relation      164
Congruent      25 43 405
Congruent matrices      285
conic      283 296 316
Conjugate algebraic numbers      448
Conjugate complex numbers      117
Conjugate diameter      308
Conjugate in a group      158
Conjugate quaternions      257
Conjugate subfields      474
Conjugate subgroups      163
Conjugate vector space      210
Consistency principle      359
Constructive proof      92
Contain (a set)      358
Content of polynomial      86
Continuum, cardinal number of      387
Coordinates of vectors      193 209 262
Coordinates, change of      260ff.
Coordinates, homogeneous      313
Coset      146 207
Countable set      384 436
Cover (in partial order)      372
Cramer's rule      325
Critical points      291
Cubic equation      119
Cubic equation, irreducible case      474
Cubic equation, trigonometric solution      102
Cut, Dedekind      104
CYCLE      150
Cyclic group      140
Cyclic permutation      150
Cyclic subspace      344
Cyclotomic equation      112
Cyclotomic polynomial      89
De Moivre formulas      111
Decimals      97
Decomposition of ideal      450
Decomposition of matrices, linear transformations      346ff.
Dedekind cut (axiom)      104
Defining relation      142
Degree      62 66
Degree of extension field      429
Degree of polynomial      62
Denumerable set      384
Dependence, linear      176
Derivative, formal      465
Determinant      48 318ff.
Determinant, rank      326
Diagonal matrix      228
Diagonal process      386 436
Diagonally dominant      323
Diagram, for partial order      372
Dihedral groups      143
Dilemma, Pythagorean      94
Dimension of vector space      169 178
Direct product      156
Direct sum      195
Direct sum of matrices      347
Direct sum of rings      396
Direct sum of subspaces      195 346
Discriminant      117
Discriminant of cubic      120
Disjunctive canonical form      369
Distance      201
Distributive lattice      363
Distributive law      2 134 170
Distributive law for Boolean algebra      362
Distributive law for cardinal numbers      390
Distributive law for matrices      224
Distributive law for sets      359
Distributive law, general      14
Distributive law, right      4
Divisible      16
Division algebra      396 414
Division algorithm      18 74 440
Division ring      256 401
Divisor      16
Divisor of zero      see "Zero divisor"
Divisor, greatest common      19
Domain      33 241
Domain, integral      3
Domain, ordered      9 98
Domain, unique factorization      84
Dual basis      210
Dual isomorphism      473
Dual numbers      397
Dual space      210
Duality principle      212 373
Dualization law      359
Duplication of cube      434
Echelon matrix      184 185
Eigenvalue      265 332
Eigenvector      265
Eisenstein's irreducibility criterion      88
Elementary column operation      248
Elementary divisors      353
Elementary matrix      243ff. 321
Elementary row operation      181
Elementary symmetric polynomial      154
Elimination      48 180
Elliptic function field      427
Epimorphic image      400
Epimorphism      399
Equality of functions      127
Equality of transformations      127
Equality, laws of      3 26
Equations      see also "Polynomial"
Equations of stable type      122
Equations, simultaneous linear      47
EQUIVALENCE      248 277
Equivalence relation      34 164
Equivalence, under a group      277ff.
Erlanger Program      132
Euclidean algorithm      18
Euclidean algorithm for Gaussian integers      441
Euclidean algorithm for polynomials      81
Euclidean group      131 276
Euclidean vector space      200ff.
Even permutation      153
Exponentiation of cardinal numbers      392
Exponents, laws of      14
Extension      45
Extension field      421
Extension field, iterated      431ff.
Factor      16
Factor group      see "Quotient-group"
Fermat theorem      28 418
Field      38 133
Field of quotients      43
Field of sets      378
Finite dimensional      178
Finite extension      429
Finite field      456ff.
Finite induction      13
Finite induction, second principle of      15
Finite set      383
Formal derivative      465
Four group      151
Full linear group      268
Fully reducible      347
Function      32
Fundamental theorem of algebra      113ff.
Fundamental Theorem of Arithmetic      23
Fundamental Theorem of Galois Theory      472
Fundamental theorem of ideal theory      450
Fundamental theorem on symmetric polynomials      154
Galileo paradox      384
Galois field      458
Galois group      459ff.
Gauss elimination      48 180
Gauss' lemma      85
Gaussian domain      see "Unique factorization domain"
Gaussian integer      439
Generation of subalgebras      369
Generators of a field extension      421
Generators of group      141
Generators of vector space      see "Span"
Gram-Schmidt process      204
Greatest common divisor      19 81 407
Greatest lower bound      96 374
Group      124ff. 133
Group of transformations      126 130
Group, abstract      133
Group, algebra      397
Group, cyclic      140
Hadamard determinant theorem      331
Hermitian form      302
Hermitian matrix      300ff.
Hilbert basis theorem      412
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте