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Artin M. — Algebra
Artin M. — Algebra

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Название: Algebra

Автор: Artin M.

Аннотация:

This is a superb book to introduce any math major to the most important ideas of abstract algebra. How often does a mathematician with the world renowned research stature of professor Artin choose to devote the time and effort to write a beginning book in essentially his specialty (he is a famous algebraic geometer), and really make the ideas understandable to the young student? Primarily when he has to teach the course, and wants a suitable source to teach from. That is apparently the genesis of this book, which took birth as class notes for the undergraduate algebra course at MIT taught several times by Professor Artin. This fine book can serve well as an introduction, or second course in algebra, at either honors or upper undergraduate level, or even first year graduate level, (although it omits one topic, multilinear and tensor algebra that grad students will eventually need). The material obviously rolls off the author's fingertips, and the reader is the beneficiary, since it all looks easy to us too, although one must definitely think along the way. With the easily defensible belief that the most important groups in mathematics are linear ones, the author begins with matrices, carries these illustrative examples throughout the treatment of groups, and even includes a beautiful introductory section on some important classical lie groups that cannot be found in any other comparable beginning algebra text. When an author is a true master, as here, he is not limited to mimicking the topics found in other successful texts but can cover each topic as he chooses and to the depth he wishes. Other unique touches are a section on divisibility in number fields, including Minkowski's geometric proof of the finiteness of the class group. This is the best modern introduction to abstract algebra available.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 618

Добавлена в каталог: 09.12.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel      570
Abelian character      325
Abelian group      451
Abelian groups, Structure Theorem      472
Addition: in a field      83
Addition: in a module      450
Addition: in a ring      346
Addition: matrix      2
Addition: vector      78 86
Adjoint matrix      29 250
Adjoint representation      304
Adjunction: of an element      365
Adjunction: symbolic      506
Affine group      306
Algebra: Fundamental Theorem of      527
Algebra: Lie      291
Algebraic closure      527
Algebraic curve      376
Algebraic curve, irreducible      386
Algebraic element      493
Algebraic extension      499
Algebraic geometry      373
Algebraic group      289 299
Algebraic integer      410
Algebraic number      345
Algebraic variety      373
Algebraically closed field      527
Algebraically dependent      525
Algebraically independent      525
Algorithm, Todd — Coxeter      223
Almost everywhere      516
Alternating group      52
Angle: between vectors      126 248
Angle: trisection of      505
Annihilator      484
Antipodal point      277
Arithmetic: Fundamental Theorem of      390
Arithmetic: modular      64
arrow      586
Arrow, wiggly      586
Ascending chain condition      393 467
Associate elements      392
Associative law      5 39
Automorphism      176
Automorphism of a field      539
Automorphism of a group      50
Averaging over a group      311
Axiomatic characterization of determinant      23
Axioms, of choice      101 374 588
Axioms, Peano      348
Baker      416
Ball, open      593
Basis: change of      98
Basis: of a module      454
Basis: of a vector space      90
Basis: orthogonal      244
Basis: orthonormal      126 241
Basis: standard      26 90 454
Basis: symplectic      261
Basis: theorem      469
Basis: transcendence      525
Bezout bound      376
Bijection      586
Bijective map      586
Bilateral symmetry      155
Bilinear form      238
Binomial coefficient      589
Biquadratic extension      539
Block multiplication      8
Block, Jordan      480
Bound, upper      588
Bounded set      595
Bracket, Lie      290 291
Branch points      521
Branched covering      378 520
Branched covering, isomorphism of      519
Bruhat decomposition      236
Bundle, vector      483
Burnside's Formula      196
Cancellation law      42 84 369
Cancellation Law for ideals      422
Canonical form, rational      479
Cantor      587
Cardano's Formula      544
Cardinality of a set      586
Case analysis      589
Cauchy — Riemann equations      598
Cayley transform      306
Cayley — Hamilton theorem      153 488
Cayley's theorem      197
Center: of a group      52
Center: of gravity      163
centralizer      198
Centrally symmetric set      426
Chain condition, ascending      393 467
Change of basis      98
Change of basis, matrix of      98
CHARACTER      316
Character group      325
Character table      320
Character, abelian      325
Character, dimension of      317
Character, irreducible      316
Characteristic polynomial      122
Characteristic subgroup      234
Characteristic value      117
Characteristic vector      117
Characteristic: of a field      86
Characteristic: of a ring      358
Chinese remainder theorem      303 441
Choice, axiom of      101 374
Circulant      268
Class equation      198
Class function      318
Class group      426
Class number      417 426
Class: congruence      56 64
Class: conjugacy      198
Class: equivalence      54
Class: ideal      417 425
Class: isomorphism      49
Class: residue      64
Classical group      270
Classification of groups      49 299
Closed set      594
Closed word      233
Closure, algebraic      527
Coefficient, leading      350
Column index      1
Column vector      2
Combination, linear      87
Commutative law      39
Commutative ring      346
Commutator      222
Commutator subgroup      234
Compact group      313
Compact set      595
Complement, orthogonal      243
Complete expansion of the determinant      28
Complete induction      380 592
Complete set of relations      464
Complex algebraic group      299
Complex representation      310
Component, connected      77
Composition, law of      39
Conductor      387
Congruence: class      56 64
Congruence: of integers      64
Congruent matrices      270
conic      255
Conjugacy class      198
Conjugate element      51
Conjugate linearity      250
Conjugate representation      309
Conjugate subfield      558
Conjugate subgroup      180
Conjugation      50 198
Connected component      77
Connected set      595
Connected, simply      278
Constructible point, line, circle      500
Constructible real number      502
Construction, ruler and compass      500
Content      399
Continuous function, map      595
Continuous representation      313
Contradiction, proof by      592
Convex set      427
Coordinate vector      94 455
coordinates      94
Correspondence theorem      75 360 452
Coset      57
Coset multiplication      68
Coset space      178
Coset, double      77
Coset, left      57
Coset, right      59
Counting Formula      58 180
Covering: branched      378 520
Cramer's rule      31
Crystal system      187
Crystallographic group      172 187
Crystallographic restriction      169
Cubic equation      543
Cubic extension      497
Cubic, resolvent      564
Curve, algebraic      376
Cut and paste      520
Cycle: decomposition      213
Cycle: notation      213
Cyclic group      46 164 184
Cyclic permutation      25
Cyclotomic field or extension      567
Cyclotomic polynomial      405
Decomposition, polar      304
Defining relations for a group      221
Definition      585
Definition, inductive or recursive      348
Degree: of a field extension      497
Degree: of a polynomial      350
Degree: of a rational function      535
Degree: of an algebraic curve      387
Degree: of an element      497
Degree: transcendence      526
Degree: weighted      550
Dependence, linear      88 101
Determinant      20 453
Determinant of an operator      123
Determinant, axiomatic characterization      23
Determinant, complete expansion of      28
Determinant, Vandermonde      36
Diagonal entries of a matrix      6
Diagonal matrix      6
Diagonalization      130 458
Dichotomy      589
Differential equation      135
Dihedral group      164 184
Dimension formula      110
Dimension: of a character      317
Dimension: of a linear group      293
Dimension: of a manifold      596
Dimension: of a representation      308
Dimension: of a vector space      93
Diophantine equation      410 437
Direct sum: of representations      315
Direct sum: of submodules      471
Direct sum: of subspaces      102
Discrete group of motions      166 167
Discriminant      548
Discriminant of a cubic      546
Discriminant of a quadratic number field      413
Distance between vectors      125
Distinct elements      585
Distributive law      5
Divide and conquer      589
Divisor      392
Divisor, greatest common      46 395
Divisor, proper      392
Divisor, zero      368
Domain: Euclidean      397
Domain: fundamental      195
Domain: integral      368
Domain: of a map      585
Domain: principal ideal      396
Domain: unique factorization      394
Dot product      125 237
Double coset      77
Double covering      277
Echelon matrix      14
Eigenvalue      117
Eigenvector      117
Eisenstein criterion      404
Element: algebraic      493
Element: associate      392
Element: conjugate      51
Element: ideal      356
Element: idempotent      382
Element: identity      41
Element: image of      585
Element: infinitesimal      365
Element: invertible      42
Element: irreducible      392
Element: maximal      588
Element: nilpotent      365
Element: norm of      414
Element: of a field extension, primitive      552
Element: of a lattice, primitive      172
Element: order of      47
Element: prime      395
Element: representative      55
Element: transcendental      493
Element: unipotent      381
Element: unit      347
Elementary column operation      18
Elementary matrix      11
Elementary row operation      12
Elementary symmetric function      547
Elements: distinct      585
Elements: independent      454
Elimination, Gaussian      12
Ellipsoid      258
Entries: diagonal      6
Entries: of a matrix      1
Equation: class      198
Equation: Diophantine      437
Equation: homogeneous      16
Equation: linear      4
Equation: quartic      560
Equation: quintic      570
Equations, Cauchy — Riemann      598
Equivalence class      53
Equivalence relation      53
Equivalence relation, determined by a map      55
Eratosthenes, sieve of      403
Euclidean Domain      397
Euclidean space      247
Euler      410
Evaluation of polynomials      353
Even permutation      26
Exceptional group      299
1 2 3 4 5
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