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Lang S. — Undergraduate Algebra
Lang S. — Undergraduate Algebra

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Название: Undergraduate Algebra

Автор: Lang S.

Аннотация:

Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.
For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder’s proof of the Mason-Stothers polynomial abc theorem.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-rd

Год издания: 2005

Количество страниц: 385

Добавлена в каталог: 06.04.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Pos_{n}$      252
$SL_2$      239
$SL_n$      245 251—257
abc conjecture      171
abc polynomial      167
Abelian extension      283 296
Abelian group      17 67
Absolute value      328 342 348
action      73
Additive group      17
Adic expansion      13
Adjoin      261
Adjoint      251
Affine group or map      232
Algebra      256
algebraic      258 302
Algebraic closure      252 302 348
Algebraic extension      302
Algebraic integer      322
Algebraic number      380
Algebraically closed      115 262
Algebraically independent      157
Alternating group      65
Arbitrarily large      330
Archimedean      331
Artin's conjecture      316
Artin's theorem      220 286
Associated linear map      191
Associativity      16
Asymptotic      10
Automorphism      91 104
Automorphism of field      277
Automorphism of group      36 96
Automorphism of ring      90
Automorphism of vector space      187
Axiom of Choice      358
Baker conjecture      172
Base change      264
Base field      264
Basis      180 200 205 357
Bernstein's theorem      361
Bijective      27
Bimultiplicative      291
Binomial coefficient      5 15
Borel subgroup      237 240
Bracket action      231
Bracket product      231 256
Bruhat decomposition      237
Canonical homomorphism      46 48 204
Cardinality      359
Cartan decomposition      253
Cauchy sequence      307 325 330
Cayley — Hamilton theorem      227
Center      52 74 87 192
centralizer      75
Characteristic      95 310
Characteristic polynomial      217 219
Characters      231 255 256
Chevalley's Theorem      158
Chinese Remainder Thorem      14 71 97
Circle group      47
Class field theory      322
Class formula      78
Coefficients of polynomial      106 110 136
Common divisor      5
Commutative      17 64 84
Commutator subgroup      53 241
Commutators      53
Complement      353
complete      331
Completion      307 325 342
complex numbers      346
Component      188
Composite field      262 288
Composite mapping      28
Congruence      12 47 91 92
Conjugacy class      76
conjugate      53 275
Conjugate elements or fields      275
Conjugate roots      271
Conjugation      37 53 74
Conjugation action      74 231 254
Constant term      110
Continuity of the roots      142
Converge      331
Convolution      99
Coordinate      180
Coordinate maps      32
Coordinate vector      180
Coset      41
Coset decomposition      42
Coset representative      42
Covering      362
Cubic extension      292
Cubic polynomial      162 292
CYCLE      60 66
Cyclic extension      283
Cyclic group      22 26 55 115
Cyclic module      210
Cyclotomic equation      124
Cyclotomic polynomial      127
Davenport's theorem      170
Decimal expansion      343
Decomposition formula      77
Degree of element      259
Degree of extension      259
Degree of polynomial      108 110 153
Denominator      9
Dense      342
Denumerable      359
Derivation      100
Derivative      123
Diagonalize      217
Differential equations      223
DIMENSION      186
Direct product      18 198
Direct sum      38 71
Discriminant      63 161 292
Disjoint sets      353 362
Distributive law      85
Divide      5 119 144
Division ring      198
Divisor of zero      86
Eigenspace      216
Eigenvalue      215 233
Eigenvector      215 233
Eisenstein criterion      139 149
Element      1
Elementary symmetric polynomials      159
Embedding      35 102 267
Empty set      1
Endomorphism      84 184 194
Equivalence class      12
Equivalence relation      12
Euclidean algorithm      4 113
Euler phi function      14
Evaluation      109 155
Even permutation      65
Exact      201
EXPONENT      22 40 67 210
Extension of embedding      268 270
Extension of fields      258
Factor group      45
Factor module      203
Factor ring      93
Factor space      204
Factorial ring      144
Factorization      122 144
Family      351
Fan      235
Feit — Thompson theorem      49
Fermat's theorem      128 168
Field      86
Finite abelian group      67
Finite extension      258
Finite field      117 309
Finite group      18
Finite index      43 51
Finite order      22
Finite period      23
Finite set      378
Finitely generated      208 210
Fixed field      275 277
Free Abelian group      208
Free group      325
Free module      200
Frey      173
Frobenius automorphism      313
Galois extension      280
Galois group      281
Gauss' lemma      139 147
General linear group      139 147 232
Generalized Szpiro conjecture      173
Generators      6 20 88 109 157 179 193 261 357
Geometry      31
GL      187 232
Greatest common divisor      5 119 144
Greatest element      355
Group      16
Groups of order eight      24 25
Hall conjecture      172
Hermitian      252
Homogeneous polynomial      153 159
Homomorphism of groups      33 38
Homomorphism of modules or vector spaces      182 194
Homomorphism of rings      90
Ideal      6 87
Identity      28 189
Image      26
inclusion      28
Independent variables      157
INDEX      43 51
indexed      351 352
Induced homomorphism      47 76
Induced ordering      326
Induction      2
Inductively ordered      356
Inequalities      327
Infinite cyclic      22
Infinite period      23
Infinite set      379
Injective      27
Inner automorphism      38 40
Integers      1 373
Integral ring      86
Integral root      141
Intersection      352
Invariant subspace      222 229
Inverse      17
Inverse image      31 32 35 353
Inverse map      28 183
Invertible      232
Irreducible      120 139 140 141 143 259
Isometry      30
Isomorphism      35 90 91 184 231 267
Isotropy group      75
Iwasawa decomposition      246 251
Jordan Basis      226
Jordan normal form      227
Kernel      34 90 183 194
Kummer symbol      290
Law of composition      16
Leading coefficient      110
Least common multiple      14
Least upper bound      331 355
Left coset      41
Left ideal      87
Leibniz rule      231 256
Length of module      107 213
Lie algebra      231 256
Lie product      231
LIMIT      331
Linear map      182 194
Linear polynomial      111
Linearly dependent      179
Linearly independent      179 357
Logarithmic derivative      127
Mapping      26
Mason — Stothers theorem      128 167
Masser — Oesterle      171
Mat      188
Matrix      188
Maximal element      355
Maximal ideal      96 99
Maximal subset of linearly independent elements      181
Minimal polynomial      221
Module      192
Module over principal ring      210
MODULO      12 45 93
Moebius function      99 127
Monic      122
Monomial      153
Morphism      91 230
Multiple root      122 165
Multiplication table      24
Multiplicative function      99
Multiplicative group      16
Multiplicity of root      122
Natural number      373
Negative      326
Nilpotent      87 97 234
Non-archimedean      343
Norm      274
Normal extension      278
Normal subgroup      45
Normalized factorization      122
normalizer      52 75
Null sequence      307 325 334
Numerator      9
Odd permutation      65
Onto      27
Operation      73
Orbit      75
Orbit decomposition      77
Order at a prime      146
Order of a group      18 43
Order of a set      2
Order of linear group      235
Order of orbit      77
Order preserving      327
Ordering of ring      326
Ordering of sets      354 375
Over      268 275
p-adic      134 306 308 343
p-group      67
p-subgroup      79
p-Sylow group      79
Partial fraction      129 131
Partial ordering      354
Period      23 210
Permutation      28 30 43
PGL      237 239
Polar decomposition      253
Polynomial      106 152
Polynomial function      108 155
Polynomial ring      106 108
Polynomials and matrices      220
Positive      326
Positive definite      252
Prime      10 143 148
1 2
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