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Hazewinkel M. (ed.) — Handbook of Algebra, Volume 4

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Название: Handbook of Algebra, Volume 4

Автор: Hazewinkel M. (ed.)

Аннотация:

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest.

In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2006

Количество страниц: 518

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-diagram      347
-group      474
-group      474
$K(\pi, 1)$ -space      363 452
      5
      5
      5
      416
      390
-group      481 482
$\alpha$ -transformation      440
$\mathcal{A}$ -leader      255
$\mathcal{E}$ -subvariety      264
$\mathcal{E}$ -variety      263
$\mathcal{E}$ -variety over a $\sigmaA*$ -field      266
$\mathcal{U}$ -variety      263
$\Omega$ -spectrum      11
$\Phi$ -group      483—485
$\Phi$ -Sylow torus      344
$\Phi$ -torus      343
$\Phi_0$ -group      485
$\pi$ -minimality      478
$\sigma *$ -linearly independent      275
$\sigma$ - field      245
$\sigma$ -algebra      290
$\sigma$ -algebraic      250 252 280
$\sigma$ -algebraic field extension      250 280
$\sigma$ -algebraically dependent      250
$\sigma$ -algebraically independent      250 280 296
$\sigma$ -algebraically independent, indexing      296
$\sigma$ -algebraically independent, set      296
$\sigma$ -automorphism      247
$\sigma$ -compositum      249
$\sigma$ -dimension      271
$\sigma$ -domain      312
$\sigma$ -endomorphism      247
$\sigma$ -factor ring      247
$\sigma$ -field extension      245
$\sigma$ -field of fractions      250
$\sigma$ -Galois group      314
$\sigma$ -generators of a $\sigma$ -ideal      246
$\sigma$ -homomorphism      247 269
$\sigma$ -homomorphism of D-modules      269
$\sigma$ -homomorphism of filtered $\sigma*$ -R-modules      274
$\sigma$ -ideal      245
$\sigma$ -indeterminate      250 296
$\sigma$ -invariant      314
$\sigma$ -invariant subgroup      314
$\sigma$ -isomorphic      295
$\sigma$ -isomorphism      247
$\sigma$ -K-algebra      290
$\sigma$ -negative      441
$\sigma$ -normal      317 318
$\sigma$ -normal extension      317 318
$\sigma$ -operator      268
$\sigma$ -overfield      245 252
$\sigma$ -overfield of finite degree      311
$\sigma$ -overring      245 312
$\sigma$ -place      312
$\sigma$ -positive      441
$\sigma$ -quotient ring      247
$\sigma$ -R-module      268
$\sigma$ -ring of fractions      250
$\sigma$ -specialization      312
$\sigma$ -stable      314
$\sigma$ -stable subgroup      314
$\sigma$ -subring      245
$\sigma$ -subring of periodic elements      302
$\sigma$ -subring of R generated by the set B over       247
$\sigma$ -subset      249
$\sigma$ -transcendence basis      280 282 293
$\sigma$ -transcendence degree      281 282 290
$\sigma$ -transcendental      250
$\sigma$ -type      271 282
$\sigma$ -valuation      312
$\sigma$ -valuation, ring      312
$\sigma$ -vector space      268
$\sigma*$ -field of residue classes      291
$\sigma*$ -algebra      290
$\sigma*$ -algebraically dependent      280
$\sigma*$ -algebraically independent      251
$\sigma*$ -dimension polynomial      273 275 283 285
$\sigma*$ -dimension polynomial of a system of $\sigma*$ -equations      286
$\sigma*$ -dimension polynomial of an ideal      285
$\sigma*$ -field      245
$\sigma*$ -field extension      245 247
$\sigma*$ -generators      247
$\sigma*$ -ideal      245 286
$\sigma*$ -indeterminates      251 256
$\sigma*$ -K-algebra      290
$\sigma*$ -linearly dependent      275
$\sigma*$ -overfield      245 252
$\sigma*$ -R-module      272
$\sigma*$ -ring      245
$\sigma*$ -ring of fractions      250
$\sigma*$ -subfield      245
$\sigma*$ -subring      245
$\sigma*$ -subset      249
$\sigma*$ -type      283
$\sigma*$ -vector space      291
$\sigma_i$ -negative      441
$\sigma_i$ -positive      441
$\Sigma_m$ -algebra structure      454
(2, 3)-generated group      387
(2, 3, 7)-generated      415
(2, 3, 7)-generated group      387 397
(2, 3, 7)-generating triple      391 399 408 415
(2, 3, 7)-generators      397
(2, 3, k)-generated      410 415
(2, 3,k)-triple      403
(k, l, m)-generated      388
(k, l, m)-generating triple      388
(k, l, m)-triple      388
2-cocycle      192 199
2-cocycle deformation      217
Abstract triangle group      388
Acyclic      14
Acyclic complex      23
Acyclic simplicial group      10
Acyclic simplicial ring      10
Additivity theorem      5 24
Adian theorem      490
Adian, S.I.      479 487
Adjoint action      124 187 214 221
Admissible epimorphism      15
Admissible monomorphism      15
Affine algebraic group      176
Affine algebraic variety      87
Affine group scheme      176 226
Affine quotient      203
Affine reflection      374
Affine Weyl group      358 374
Alexander polynomial      368
Alexander theorem      366
Algebra of $\sigma$ -polynomials      250
Algebra of $\sigma*$ -polynomials      251 256
Algebra of difference polynomials      250
Algebra of generalized characters      190
Algebra of inversive difference polynomials      251
Algebra of lowering and raising operators      121
Algebra of symmetric functions      340
Algebraic $\sigma$ -overfield      306
Algebraic $\sigma*$ -equation      252 286
Algebraic closure      40 294 299
Algebraic geometry      175
Algebraic group      194 203 361
Algebraic matrix group      316
Algebraic solution      253 254
Algebraic solution of a set of $\sigma$ -polynomials      253
Algebraic subset      325

Algebraic vector bundle      16
Algebraically independent      292
Algebraically irreducible $\sigma$ -polynomial      299
Almost centralizing extension      87
Almost cocommutative      189
Almost every solution      305
Almost every specialization      305
Almost every specialization has a property $\mathcal{P}$       305
Almost layer-finite      485
Almost locally soluble      475
Almost locally soluble, group      479 488
Almost nilpotent group      483
Alt(?)      415
Alternating group      391
Analytic isomorphism      30
Annuls      252
Anti-Chern character      6 46
Antipode      175 182 196
Aperiodic $\sigma$ -field      267
Arithmetic Fuchsian group      411
Arnold, V.I.      429 453 454
Artin braid group      362 368
Artin group      430 444
Artin group of crystallographic type      368
Artin presentation      436
Artin, E.      365 429 435
Artin-Brieskorn braid group      444
Artin-Brieskorn group      444 445
Artinian $\sigma*$ -ring      273
Artinian difference ring      269
Ascending chain condition      260
Ascending filtration      268
Associate graded $\mathcal{D}$ -module      269
Associativity isomorphism      209
Auslander purity of the branch locus      341
Automatic group      445
Automorphism group      429
Automorphism group of a free group      413 434
Automorphism group of an algebraic curve      387
Automorphism of permutation-conjugacy type      449
Autoreduced      277
Autoreduced set      255
Autoreduced set of $\sigma*$ -polynomials      257
Autoreduced set of differential polynomials      256
Autoreduced set of inversive difference polynomials      258
Autoreduced set of lowest rank      258
Autoreduced subset of lowest rank      256 278
Averaging element      184
Averaging map      187
B type pattern      162
b-invariant      369
Babbitt decomposition      307
Bad prime      357
Baer, R.      472
Baez — Birman monoid      431 450
Baez, J.      431
Baird, G.E.      111
Bakhova, M.Yu.      469
Base      439
Basic invariants      341
Basic set      244
Basis      260 316
Basis for transformal transcendence      280
Bass, H.      5
Beilinson motivic cohomology      41
Benign $\sigma$ -field extension      306
Bernoulli numbers      34 51
Bernstein inequality      79 88
Betweenness condition      117 127
Bi-Galois object      202 210
Biadditive      66
Bialgebra      175 181 182
Bialgebra algebra      202
Bialgebra in a braided category      218
Bialgebra in a braided tensor category      219
Bialgebra, homomorphism      182
Biautomatic      445
Bicharacter      190
Biedenharn, L.C.      111
Biexact      66
Big etale site      39
Big Zariski site      39
Bigelow, S.      442
Biideal      182
Bijectivity of the antipode      219
Binary finite      469 470
Binary finite group      479
Binary finiteness      469
Binary soluble      474
Biprimitive finiteness      469 471
Biprimitively finite      469
Biproduct      193 220
Birch, B.      52
Bireflection      374
Birman — Murakami — Wenzl algebra      443
Birman, J.S.      431 436 441 443 450
Bloch cycle group      43
Bloch higher Chow group      6 43
Bloch — Kato conjecture      5 38 42
Bonsfield — Kan construction      9
Borel regulator      52
Borel subalgebra      140 147
Borel subgroup      361
Borel, A.      44 52
Bosonization      193 220
Bott periodicity      9
Bounded chain complex      21 23 58
Bounded complex      23
Braid      429 431
Braid group      211 340 362 365 368 373 374 429
Braid group in the solid torus      430
Braid group of a complex reflection group      362
Braid group of a group action      444
Braid group of a handlebody      446
Braid group of a solid torus      446
Braid group of a sphere      446
Braid group of the action of W on Y      444
Braid group of the sphere      430
Braid group on n strings      366
Braid group relations      448
Braid groups in 3-manifolds      430
Braid groups in handlebodies      430
Braid groups of Riemann surfaces      430
Braid monoid      365
Braid relation      212
Braid-permutation group      431 448
Braided category      210
Braided Hopf algebra      188 219
Braided monoidal category      217
Braided tensor category      210 211 214 219
Braiding      190 229
Braiding structure      219
Branching rule      111—113 116 117 120 142 154 159
Bratteli diagram      113
Brauer character      406 409
Brauer group      34 37 40 217
Brauer — Long group      217
Brieskorn, E.      430 444 445 453 454
Bruhat cell      362
Bruhat decomposition      351 361
Bruhat order      350
Bruhat — Chevalley order      350 362
Burau relations      437
Burau representation      368 429 430 442
Burau, W.      437
Burnside group      484
Burnside p-group      487
Burnside problem      487
C*-algebra      175 197
Cancellation law      350

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