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Herstein I.N. — Topics in algebra
Herstein I.N. — Topics in algebra

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Название: Topics in algebra

Автор: Herstein I.N.

Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2

Год издания: 1975

Количество страниц: 400

Добавлена в каталог: 16.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$2\times 2$ rational matrices, ring of      123
$n\times n$ matrix(ces) over F      278
$n\times n$ matrix(ces) over F, algebra of all      278 279
(i, j) entry      277
15—gon, regular      232
17—gon, regular      232
9—gon, regular      232
Abel      237 252 256
Abelian group      28
Abelian group, structure of finite      109 204
Abelian group, structure of finitely generated      203
Adjoint(s)      318 321
Adjoint(s), Hermitian      318 319 322 336 339 340
Adjoint(s), quaternions      372
Adjunction of element to a field      210
Albert      356 377
Algebra      262
Algebra of all $n\times n$ matrices over F      278 279
Algebra of linear transformations      261
Algebra, algebraic division      368
Algebra, boolean      9 130
Algebra, fundamental theorem of      337
Algebra, linear      260
Algebraic division algebra      368
Algebraic element      209 210
Algebraic extension      213
Algebraic integer      215
Algebraic number(s)      214—216
Algebraic of degree n      212 213
Algorithm, division      155
Algorithm, Euclidean      18
Algorithm, left-division      373
Alperin      119
Alternating group      80 256
Angle, trisecting      230
Annihilator of a subspace      188
Artin      237 259 378
Associates      146 162
Associative law(s)      14 23 27 36
Associative ring      121
Automorphism(s) of a cyclic group      66 67
Automorphism(s) of K relative to F      239
Automorphism(s) of the field      237
Automorphism(s), fixed field of a group of      238
Automorphism(s), group of inner      68
Automorphism(s), group of outer      70
Automorphism(s), inner      68
Axiom of Choice      138 367
Basis(es)      177 180
Basis(es), dual      187
Basis(es), orthonormal      196 338
Bessel inequality      200
Binary relation      11
Birkhoff      25
Birkhoff, G.D.      362
Boolean algebra      9 130
Boolean ring      130
Brauer — Cartan — Hua theorem      368
Burnside      119
Cancellation laws      34
Canonical form(s)      285
Canonical form(s), Jordan      299 301 302
Canonical form(s), rational      305 306 308
Cardan's formulas      251
Cartesian product      5 6
Cauchy      61 86 87
Cauchy's theorem      61 87
Cayley      71
Cayley — Hamilton theorem      263 309 334 335
Cayley's theorem      71 262
Center of a group      47 68
centralizer      47
Characteristic of integral domain      129 232 235 357
Characteristic polynomial      309 332
Characteristic root(s)      270 286—289
Characteristic root(s), multiplicity of      303
Characteristic subgroup      70
Characteristic vector      271
Characteristic zero      129 232 235
Choice, axiom of      138 367
Class equation      85 361
Class(es), congruence      22 353 354
Class(es), conjugate      83 89 361
Class(es), equivalence      7
Class(es), similarity      285
Closure under operation      27
Coefficients      153
Cofactor      334
Column of a matrix      277
Combination, linear      177
Commutative group      28
Commutative law      23
Commutative ring(s)      121
Commutative ring(s), polynomial rings over      161
Commutator      252
Commutator subgroup(s)      65 70 117 252 253
Companion matrix      307
Complement      5
Complement, orthogonal      195
Complex vector space      191
Composition of mappings      13
Congruence class      22 353 354
Congruence modulo a subgroup      39
Congruence modulo n      22
Congruent      352
Conjugacy      83
conjugate      83
Conjugate class(es)      83 89 361
Conjugate elements      83
Conjugate subgroups      99
Construction with straightedge and compass      228
Construction, invariant      187 188
Constructive      228 230
Constructive number      228
Content of polynomial      159 163
Correspondence, one-to-one      15
Coset, double      49 97 98
Coset, left      47
Coset, right      40
Cramer's rule      331
Criterion, Eisenstein      160 240 249
Criterion, Euler      360
Cube, duplicating of      231
Cycle decomposition      78
Cyclic group      30 38 49
Cyclic group, generator of      48
Cyclic module      202
Cyclic subgroup      38
Cyclic subspace      296 306
Cyclotomic polynomial      250 362
De Morgan rules      8
Decomposable set of linear transformations      291
Decomposition, cycle      78
Definite, positive      345
Degree n of an extension      208
Degree n of polynomial      154 162
Degree n, algebraic of      212 213
Degree n, alternating group of      80 256
Degree n, general polynomial of      251
Degree n, symmetric group of      28 75 241 253—257 284
Derivative      158 232 233
Desargues' theorem      361
Determinant      322
Determinant of linear transformation      329
Determinant of matrix      324
Determinant of system of linear equations      330
Diagonal matrix      282 305
Diagonal subset      6
Diagonalizable      305
Dickson      356
Difference module      202
Difference set      5
Dihedral group      54 81
DIMENSION      181
Diophantos      356
Direct product of groups      103
Direct product of groups, external      104 105
Direct product of groups, internal      106
Direct sum of modules      202
Direct sum, external      175
Direct sum, internal      174 175
Disjoint sets      4
Disjoint sets, mutually      5
Distributive law(s)      23 121
Divisibility      144 145
Division algebra, algebraic      368
Division algorithm for polynomials      155
Division ring      126
Division ring, finite      360
Divisor(s)      18
Divisor(s), elementary      308 309 310
Divisor(s), greatest common      18 145
Domain, integral      126
Domain, unique factorization      163
Dot product      192
Double coset      49 97 98
Dual basis      187
Dual space      184 187
Dual, second      188
Duplicating the cube      231
Eigenvalue      270
Eisenstein criterion      160 240 249
Element(s), algebraic      209 210
Element(s), conjugate      83
Element(s), identity      27 28
Element(s), order of      43
Element(s), order of (in a module)      206
Element(s), period of      43
Element(s), prime      146 163
Element(s), separable      236
Elementary divisors of a linear transformation      308 309 310
Elementary symmetric functions      242 243
Empty set      2
Equality of mappings      13
Equality of sets      2
Equation(s), class      85 361
Equation(s), linear homogeneous      189 190
Equation(s), rank of system of linear      190
Equation(s), secular      332
Equivalence class      7
Equivalence relation      6
Euclidean algorithm      18
Euclidean rings      143 371
Euler      43 356 376
Euler criterion      360
Euler phi-function      43 71 227 250
Even permutation      78 79
Extension, algebraic      213
Extension, degree of      208
Extension, field      207
Extension, finite      208—212
Extension, normal      244—248
Extension, separable      236 237
Extension, simple      235 236
External direct product      104 105
External direct sum      175
Fermat      44 144 149 152 356 366 371
Fermat theorem      44 152 366
Fermat theorem, little      44 366
Field(s)      126 127 207
Field(s) of quotients      140
Field(s) of rational functions      162 241
Field(s) of rational functions in n-variables      241
Field(s) of symmetric rational functions      241
Field(s), adjunction of element to      210
Field(s), automorphism of      237
Field(s), extension      207
Field(s), finite      122 356
Field(s), perfect      236
Field(s), splitting      222—227 245
Finite abelian group(s)      109
Finite abelian group(s), fundamental theorem of      109 204
Finite abelian group(s), invariants of      111
Finite characteristic      129
Finite dimensional      178
Finite extension      208—212
Finite field      122 356
Finite group      28
Finitely generated abelian group      202
Finitely generated modules      202
Finitely generated modules, fundamental theorem on      203
Fixed field of group of automorphisms      238
Form(s), canonical      285
Form(s), Jordan canonical      299 301 302
Form(s), rational canonical      305—308
Form(s), real quadratic      350
Form(s), triangular      285
Four-square theorem      371
Frobenius      356 368 369
Frobenius theorem      369
Functional, linear      187 200
Functions, elementary symmetric      242 243
Functions, rational      162 241
Functions, symmetric rational      241
Fundamental theorem of algebra      337
Fundamental theorem of finite abelian groups      109 204
Fundamental theorem of finitely generated modules      203
Fundamental Theorem of Galois Theory      247
Galois      50 207
Galois group      237
Galois theory      237—259
Galois theory, fundamental theorem of      247
Gauss' lemma      160 163 164
Gaussian integers      149
Gelfond      216
General polynomial of degree n      251
Generator of cyclic group      48
Gram — Schmidt orthogonalization process      196
Greatest common divisor      18 145
Group(s)      28
Group(s) of automorphisms of K over F      239
Group(s) of automorphisms, fixed field of      238
Group(s) of inner automorphisms      68
Group(s) of outer automorphisms      70
Group(s), Abelian      28 109 203 204
Group(s), alternating      80 256
Group(s), automorphism(s) of      66 67
Group(s), center of      47 68
Group(s), commutative      28
Group(s), cyclic      30 38 49
Group(s), dihedral      54 81
Group(s), direct product of      103
Group(s), factor      52
Group(s), finite      28
Group(s), Galois      237
Group(s), generator of cyclic      48
Group(s), homomorphism(s) of      54
Group(s), isomorphic      58
Group(s), isomorphism(s) of      58
Group(s), nilpotent      117
Group(s), order of      28
Group(s), permutation      75
Group(s), quaternion units      81
Group(s), quotient      52
Group(s), simple      60
Group(s), solvable      116 252
Group(s), symmetric      28 75 241 253—257 284
Hall      119
Halmos      206 354
Hamilton      124 334 356
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