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Dummit D.S., Foote R.M. — Abstract algebra
Dummit D.S., Foote R.M. — Abstract algebra

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Название: Abstract algebra

Авторы: Dummit D.S., Foote R.M.

Аннотация:

The principal change from the second edition is the addition of Grobner bases to this edition. The basic theory is introduced in a new Section 9.6. Applications to solving systems of polynomial equations (elimination theory) appear at the end of this section, rounding it out as a self-contained foundation in the topic. Additional applications and examples are then woven into the treatment of affine algebraic sets and Jt-algebra homo-morphisms in Chapter 15. Although the theory in the latter chapter remains independent of Grobner bases, the new applications, examples and computational techniques significantly enhance the development, and we recommend that Section 9.6 be read either as a segue to or in parallel with Chapter 15. A wealth of exercises involving Grobner bases, both computational and theoretical in nature, have been added in Section 9.6 and Chapter 15. Preliminary exercises on Grobner bases can (and should, as an aid to understanding the algorithms) be done by hand, but more extensive computations, and in particular most of the use of Grobner bases in the exercises in Chapter 15, will likely require computer assisted computation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 2004

Количество страниц: 932

Добавлена в каталог: 07.02.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\mathbb Z/n\mathbb Z)^x$      10 18 61 135 267 314 596
$B^n(G; A)$      see «Coboundaries
$C^n(G; A)$      see “Cochains”
$Ext_R^n(A, B)$      779ff
$GL_3(\mathbb F_2)$      211ff 489 644
$Hom_F(V, M)$      416
$Hom_R(M, N)$      345ff 385ff
$H^n(G; A)$      see “Cohomology group”
$p^{th}$-power map      166 174
$Tor_n^R$      788ff
$Z^n(G; A)$      see “Cocycles”
$\mathbb Q$, subgroups of      65 198
$\mathbb Z/n\mathbb Z$      17 56 75ff 226 267
$\mathbb Z[(1+\sqrt{-19})/2]$      277 280 282
$\mathbb Z[i]$      see “Gaussian integers”
$\mathbb Z[\sqrt 2]$      278 311
$\mathbb Z[\sqrt{-5}]$      273 279 283ff
$\mathbb {Q/Z}$      86
1-parameter subgroup      505
2-stage Euclidean Domain      294
A.C.C.      see “Ascending chain condition”
Abelian      17
Abelian categories      791
Abelian extensions of $\mathbb Q$      599ff
Abelian group      17 84 158ff 196 339 468
Abelian group, representation of      861
Abel’s Theorem (insolvability of quintic)      625
Absolutely flat      797
Action, faithful      43 112ff
Action, faithful group      41ff 112ff 451
Action, faithful group ring      842
Action, faithful left vs. right      128 156
Adjoint Associativity      401 804 811
Affine algebraic sets      658ff
Affine k-algebra      734
Affine n-space      338 658
Affine scheme      742
Afflne curve      726
Affords a representation      114 843
Algebra      342ff 657
Algebraic closure      543
Algebraic closure of a finite field      588
Algebraic conjugate      see “Conjugate”
Algebraic geometry      330 655ff 658 742 745 760 762 911
Algebraic, element      520ff 527
Algebraic, element extension      520ff 527
Algebraic, element integer      695ff 887
Algebraic, element number      527
Algebraically closed      543
Algebraically conjugate characters      878
Algebraically independent      645 699
Algebraically indistinguishable      518
Algorithm for Jordan Canonical Form      496
Algorithm for rational canonical form      481
Alternating form      437
Alternating group      107ff 611
Alternating group $A_4$      110 111
Alternating group $A_5$ simplicity of      127 145
Alternating group, characters of      883
Alternating group, simplicity of      110 149ff
Alternating tensor      451
Alternating, function      436 446
Angle trisecting      535 535
Annihilated by      338
Annihilator      249
Annihilator of a submodule      344 460
Annihilator of a subspace      434 435
arrow      912
Artin — Schreier extensions      589 636
Artin — Schreier map      623
Artinian      657 750ff 855
Ascending chain condition (A.C.C.)      458 656ff
Assassin      670
Associate      284ff
Associated primes of a module      670 730 748
Associated primes of a prime ideal      685
Associated primes of an ideal      682
Associative      16
Asymptotic behavior      508
Augmentation, ideal      245 253 255 258 846
Augmentation, map      245 255 799 811
Augmented matrix      424
Aut $(\mathbb{R/Q})$      567
Automorphism      41 133ff
Automorphism group      41 133ff
Automorphism of $D_8$      136 220
Automorphism of $Q_8$      136 220ff
Automorphism of $S_6$      221
Automorphism of $S_n$      136ff
Automorphism of a field      558ff
Automorphism of a field extension      558ff
Automorphism of acyclic group      61 135 136 314
Automorphism of an elementary abelian group      136
Autonomous system      507
Baer’s Criterion      396
Balanced map      365ff
Bar resolution      799
Base field      511
Basic open set      738
Basis      354
Basis free      218 354
Basis of a field extension      513
Basis of a vector space      408
Bass’ Characterization of Noetherian Rings      793
Belongs to an ideal      682
Berlekamp’s Factorization Algorithm      311 589ff
Betti number      159 464
Bezout Domain      274 283 294 302 307 775
Bijection      2
Bilinear      368ff 372 436
Bimodule      366 404
Binary, operation      16
Binary, relation      3
Binomial theorem      60 249 548
Biquadratic, extension      530 582 589
Biquadratic, polynomial      617
Block      117
Block diagonal      423 475
Block upper triangular      423
Boolean ring      231 232 249 250 258 267
Brauer group      836
Buchberger’s Algorithm      324ff
Buchberger’s Criterion      324ff 332
Building      212
Building-Up Lemma      411
Burnside’s $p^aq^b$ Theorem      196 886ff
Burnside’s Basis Theorem      199
Burnside’s Lemma      877
Burnside’s N/C-Theoiem      213
Cancellation laws      20
Canonical forms      457 472
Canonical model      734
Cardano’s Formulas      630ff 638ff
Cardinality      1
Cartesian product      1 905ff
Castelnuovo’s Theorem      646
Casus irreducibilis      633 637
Category      391 911ff
Cauchy’s Theorem      93 96 102 146
Cayley — Hamilton theorem      478
Cayley’s Theorem      118ff
Center of a group ring      239
Center of a matrix ring      239 834 856
Center of a ring      231 231 344 832ff 856
Center of ap-group      125 188
Center, of a group      50 84 89 124 134 198
Central idempotent      357 856
Central product      157 169
Central simple algebra      832ff
Centralize      94
centralizer      49ff 123ff 133ff
Centralizer of a cycle      173
Centralizer of a representation      853
Chain complex      777
Chain complex homotopy      782
Change of basis      40 419
Changing the base      see “extension of scalars”
Character of a representation      866
Character table      880ff
Character table of $A_4$      883
Character table of $D_8$      881
Character table of $Q_8$      882
Character table of $S_3$      881
Character table of $S_4$      883
Character table of $S_5$      884
Character table of $\mathbb Z/2\mathbb Z$      880
Character table of $\mathbb Z/3\mathbb Z$      881
Character, of a group      568 866
Characteristic function      249
Characteristic of a ring      250
Characteristic p fields      510
Characteristic polynomial      473
Characteristic subgroup      135ff 174
Characteristic, of a field      510
Characters of      880 881
Chinese remainder theorem      246 265ff 313 357 768
Choice function      905
Class equation      122ff 556
Class field theory      600
Class function      866 870
Class group      761 774
Class number      761
Classical Greek Problems      531ff
Classification theorems      38 142ff 181ff
Closed points      733
Closed, topologically      676
Closed, under an operation      16 242 528
Coboundaries      800
Cochain      777 799 808
Cochain complex      777
Cochain homotopy      792
Cocycle      800
Codomain      1
Coefficient matrix      424
Cofactor      439
Cofactor, Expansion Formula      439
Cofactor, Formula for the Inverse of a Matrix      440
Coherent module sheaf      748
Cohomologically trivial      802 804 812
Cohomology group      777 798ff
Cohomology of      801 811
Coinduced module      803 811 812
Cokernel      792
Coloring graphs      335
Column rank      418 427 434
Comaximal ideals      265
Commutative      16 223
Commutative diagram      100
Commutator      89 169
Commutator series      see “Derived series”
Commutator subgroup      89 169 195ff
Commute, diagram      100
Compact      688
Compact support      225
Companion matrix      475
Compatible homomorphisms      805
Complement      180 453 454 820 829 890
complete      759ff
Complete preimage      83
Completely reducible      847
Completion      759ff
Complex conjugation      345 567 603 618 654 872
complex numbers      1 512 515 654
Component of a direct product      155 338
Composite extensions      529 591ff
Composite extensions of fields      528
Composition factors      103
Composition series      103ff
Computing Galois groups      640ff
Computing k-algebra homomorphisms      664ff
Congruence class      8ff
Congruent      8
Conjugacy class      123ff 489 860
Conjugate field      573
Conjugate of a field element      573
Conjugate of a group element      82 123ff
Conjugate of a set      123ff
Conjugate of a subgroup      134 139ff
Conjugate, algebraic      573
Conjugation      45 52 122ff 133
Conjugation in $A_n$      127 131
Conjugation in $S_n$      125ff
Connected      687
Connecting homomorphisms      778 791
Constituent of a module      847
Constructibility of a regular n-gon      534ff 601ff
Constructible      532ff
Construction of cube roots      535
Construction of the regular 17-gon      602ff
Continuous cohomology groups      809
Continuous group action      808ff
Contracting homomorphisms      809
Contraction of ideals      693 708ff
Contravariant      659
Converge      503
Coordinate ring      661
Coprime      see “Relatively prime”
Corestriction homomorphism      806 807
Corresponding group actions      129
Coset      77ff 89ff
Coset representatives      77
Cramer’s Rule      438
Criterion for the Solvability of a Quintic      639
Crossed homomorphisms      814ff
Crossed product algebra      833ff
Cubic equations, formulas for roots      630ff
Curve      726
CYCLE      29 30 33 106ff 173
Cycle decomposition      29 30 115ff 641
Cycle decomposition algorithm      30ff
Cycle type      126ff
Cycle type of automorphisms      640
Cyclic extensions      625 636
Cyclic group      22 54ff 90 149 192 198 539
Cyclic module      351 462
Cyclotomic extensions      552ff 596jff
Cyclotomic field      540ff 698
Cyclotomic polynomial      310 489 552ff
Cyclotomy      598
D.C.C.      see “Descending chain condition”
Decomposable module      847
Dedekind domain      764ff
Dedekind Domain, modules over      769ff
Dedekind-Hasse Criterion      281
Dedekind-Hasse norm      281 289 294
Degree of a character      866
Degree of a field element      520
Degree of a field extension      512
Degree of a monomial      621
Degree of a polynomial      234 295 297
Degree of a representation      840
Degree of a symmetric group      29
Degree ordering      331
Dense      677 687
Density of primes      642
Derivative of a polynomial      312 546
Derivative of a power series      505
Derived functors      785
Derived series      195ff
Descending chain condition (D.C.C)      331 657 751 855
1 2 3 4 5
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