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Moh T.T. — Algebra
Moh T.T. — Algebra

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Название: Algebra

Автор: Moh T.T.

Аннотация:

This present book comes from the first part of the lecture notes the author used for first-year graduate algebra course at the University of Minnesota, Purdue University and Peking University. The aim of this book is not only to give the student quick access to the basic knowledge of algebra, either for future advancement in the field of algebra, or for general background information, but also to show that algebra is truly a master key or "skeleton key" to many mathematical problems. The author wishes to present this book as an attempt to re-establish the contacts between algebra and other branches of mathematics and sciences. Many examples and exercises are included to illustrate the power of intuitive approaches to algebra.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 362

Добавлена в каталог: 24.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$f(x)$-adic expansion      116
$n$-th cyclotomic polynomial      280
$n$-th derived group      95
$n$-th root of unity      263
Abel      307
Abelian extension      295
Abelian group      74
Absolute value      35
Adjoint      235
Adjoint transformation      244
Affine algebraic variety      146
Affine geometry      109
Affine space      187
Al-Kashi      45
Al-Khw$\bar{a}$rizmi      6
Algebraic affine plane curve      329
Algebraic closure      145 261 271
Algebraic degree      259
Algebraic element      257
Algebraic extension      257
Algebraic geometry      125 144
Algebraic integer      152 271
Algebraic multiplicity      227
Algebraic number      256
Algebraic number theory      23
Algebraically closed      218 253
Algebraically closed field      131
Algebraically dependent      327
Algebraically independent      327
Alpian      45
Alternating group      97
Analytic geometry      187
Annihilator      197 207
Anti-linear      233
Archemedes      7 9
Archimedean property      7
Artin      329
Associative laws      6
Automorphism      73
Axiom of Choice      2 4
Basis      166 197
Betti number      208
bezout      108
Bezout’s Theorem      140
Bijective      1
Bilinear form      232
Binary operation      47
Block matrix      216
Canonical form      193
Canonical homomorphism      200
Canonical map      80
Cantor      1
Cardano      307
Cardano’s Formula      315
cardinal number      1
Cardinality      1
Castelnuovo      329
Cauchy      33
Cayley      183 224 232
Center      74
Chain      5
Chao Chha Ssu      116
Characteristic      275
Characteristic of a field      107
Characteristic polynomial      52 224
Characteristic value      224
Characteristic vector      224
Chhin Chiu — Shao      20
Chinese remainder theorem      20 208
Chiu Chang Suan Shu      166 183
Chu Shih — Chieh      108 116
Class equation      85
Classical physics      51
Clemens      329
Closed      47
Codimension      179
Coefficient ring      197
Column rank      186
Column vector      186
Common divisor      9 26 117
Common limit      37
Common multiple      9
Commutative group      74
Commutative laws      6
Commutative ring      105
Commutator subgroup      72
Companion matrix      216
Completed      43
Completion      33 262
Complex affine geometry      110
Complex integers      23
Complex projective line      71
Complexify      245
composition      303
Composition of maps      49
Composition series      86 91
Computer science      274
Congruence      13
Conic curve      56
conjugate      65
Conjugate class      75
Constructible number      264
Construction with straight-edge and compass      264
Content      122
Continuous fraction      8
Continuous function      132
Convergent Series      46
Coordinate ring      329
Coordinate system      187
Coprime      129
Corresponding polynomial      216
Coset      65
Countable      1
Countably infinite set      1
Cramer’s Rule      109
Crystallography      66
Cubic equation      307
Curve      248
Cyclic extension      295
Cyclic group      48
Cyclotomic polynomial      263
decomposed      30
Dedekind      33
Dedekind cut      39
Dedekind — Hassa theorem      151
Degree      110
del Ferro      307
Derivative      141
Descending chain condition      153
Determinant      223
Diagonal counting      3
Diagonalized      228
Dihedral group      64 88
Direct product      3 54 107 199 200
Direct sum      54 107 179 199 200
Discrete subgroup      62
Discriminant      141
Discriminant of basis      323
Disjoint union      3 58
Distance      33
Distributive laws      6
Divisor      9 26 117
Domain of definition      112
Dual      70 71
Dual basis      184
Dual space      182
E. Noether      79
Eigenvalue      224
Eigenvector      224
Elementary decomposition      210
Elementary divisor      210 215
Elementary symmetric polynomial      131
Equivalence relations      3
Euclid      6
Euclidean algorithm      6 24 114
Euclidean Domain      116 158
Euler      16 256
Euler $\phi$ function      16
Euler theorem      16
Even permutation      97
Extension      257
Faithful transformation group      59 82
Fermat      17
Fermat numbers      269
Fermat’s Little Theorem      17
Fermat’s theorem      30
Ferrari      307
Field      102
Field of rational functions      148
Field polynomial      321
Field theory      212
Finite difference      116
Finite extension      259
Finite field      103 275
Finite group      48
Finite set      1
Finitely generated      48
Finitely generated module      197 203
First isomorphism theorem      79
Fixed axis      52
Fixed field      295
Formal power series ring      113
Fractional linear transformation group      71
Free module      202
Frobinus map      276
Full linear group      54
Function field      329
Fundamental sequence      37
Fundamental theorem of algebra      218 254
Fundamental theorem of Arithmetics      10
Fundamental theorem of calculus      183
Fundamental Theorem of Finitely Generated Abelian Groups      196
Fundamental theorem of finitely generated commutative group      206
Fundamental theorem of finitely generated module over P.I.D.      205
Galilean transformation      51
Galois      47 102
Galois extension      294
Galois field      103 275
Galois group      294
Galois theorem      313
Galois theory      91
Gauss      23 166 254 268 302
Gauss lemma      123
Gaussian elimination      166
Gaussian integers      23
General linear group      52
Generalized Binomial Theorem      45
Generate      48 164
Generating set      48 164 197
Generic polynomial      131
Genus zero      125
Geometric multiplicity      227
Gibbs      233
Golden mean      190 263
Grassmann      233
Greatest common divisor      9 117
Griffith      329
Ground field      160
Group      47
H$\ddot{o}$lder      92
Hamilton      53 183 232
Hamming code      103
Heisenberg      243
hermite      232 256
Hermitian      235
Hermitian form      232
hilbert      154
Hilbert’s base theorem      154
Hilbert’s hotel      2
Hippasus      263
Homomorphism      146 199
Hsiang Chieh Chiu Chang Ssu Fa      45
Ideal      118 144
Im      77
Image      77
inclusion      1
Independent of absolute values      35
INDEX      65
Index set      3
Inertia      30
Infinite descent      125
Infinite field      103
Infinite group      48
Infinite set      1
inherited      62
Initial condition      174
Injective      1
Inner automorphism      73
Inner product      233
Inner product space      233
Integral domain      106
Interior direct sum      201
Intersection      1
Into isomorphism      73
Invariant factor      215
Invariant field      295
Invariant subgroup      74
Invariant subset      59
Invariant subspace      182 216
Irreducible complex number      27
Irreducible curve      329
Irreducible element      119
Irreducible number      10
Iskovskih      329
Isomorphic      73
Isomorphism      187
Isomorphism theorem      147
JORDAN      92
Jordan canonical form      214 219
Jordan canonical form of real matrices      221
Jordan — H$\ddot{o}$lder theorem      89
Ker      77
Kernel      77
Klein four-group      100
Kummer      105
L$\ddot{u}$roth’s theorem      327
Lagrange interpolation      22 118
Lagrange theorem      65
Lambert      256
Least common multiple      9
Left-coset      65
Leibniz      223
Length      94
Li Shun — Feng      20
Lie algebra      48
Light cone      235
Lindemann      256
Linear functional      181
Linear transformation      181
Linearly dependent      166
Linearly independent      166
Linearly independent set      197
Liouville’s theorem      254
local      112
localization      113
Long division algorithm      6
Lorentz transformation group      51
Lower triangular      231
Manin      329
Mapping      1
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