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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.
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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
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Предметный указатель
Regular element under a group action 443
Regular function 176
Regular Noetherian ring 24
Regular number 344
Regular orbit 444
Regular prime 54
Regular realization 293 295
Regular realization of a kernel 300
Regular vector 344
Regulator map 52
Reidemeister move 433 449
Reidemeister torsion 63
Reidemeister, K. 429
Relative dimension 297
Relative effective order 297
Relative limit degree 297
Relative order 297
Relatively H'-projective 68
Remainder 255
Remainder of a -field extension 305
Remainderof a -polynomial with respect to another -polynomial 255
Renormalization in quantum field theory 230
Rentschler — Gabriel — Krull dimension 83
Rentschler, R. 79 102
Replicability 305
Representation category 209
Representation theory for Hopf algebras 185
Representation theory of finite complex reflection groups 368
Representation theory of quantum affine algebras 137
Representation theory of simple Lie algebras 112
Representation theory of twisted Yangians 146
Representation theory of Yangians 137
Representations of 158
Representations of Hecke algebras 373
Representations of T(2, 3,7) 388
Representations of the Yangian Y(2) 148
Representations of twisted Yangians 158
Representations of Yangians 158
Representative function 183 212
Resco, R. 102
Residually finite-dimensional 185 205
Residue homomorphism 412
Resolution of singularities 42
Resolution Theorem 5 24
Resolutions by free filtered difference modules 276
Resolvent 303
Resolvent, ideal 303
Restricted Lie algebra 207
Restriction homomorphism 67
Return function 81 84 94
Ribbon category 211
Ribbon Hopf algebra 190 211
Riemann surface 387 390
Riemann zeta function 51
Right adjoint action 187
Right coadjoint action 216
Right derived functor 37 273
Right Galois 201
Right H-Galois 201
Right H-Galois, extension 215
Right integral 184
Right L-Galois object 202
Right Miyashita — Ulbrich action 202
Right modular element 195
Right ordered group 441
Right smash product 205
Rigid braided tensor category 211
Rigid tensor category 209 211
Rigid triple 402
Rigidity 396
Rimanyi, R. 431 448
Ring of -operators 268
Ring of constants 246
Ring of difference operators 268
Ring of differential operators 80 99 101
Ring of invariants 374 375
Ring of inversive -operators 272
Ring of inversive difference operators 272
Ring of partial difference-differential polynomials 255
Ring of S-integers 45
Ring-theoretical difference Galois theory 330
Ritt -ring 260
Ritt -ring 261
Ritt difference ring 260
Ritt number 300
Ritt — Raudenbush theorem 260
Ritt, J.F. 243
Robson, J.C. 85
Root 340
Root for a reflection 340
Root, lattice 375
Root, system 111 115 356 374
Root, system of a Kac-Moody algebra 359
Root, vector 121
Rosenfeld, A. 243
Rost 43
Round structure 63
Rourke, C 431 448 450
S formula 220
S-excision ideal 33
s-finite 469
S-torsion 29
S-torsion, object 30
Saito, K. 444 445
Saturated W-category 20
Scheme 16
Schur, algebra 373
Schur, double centralizer theorem 221
Schur, function 117
Schur, I. 117
Schur, indicator 226 227
Schur, lemma 400 402
Schur, polynomial 117
Scott formula 397 398 408
Scott, G.P. 446
Scott, L.L. 398
Second filter inequality 80 85 97
Sedova, E.I. 474 488
Seidenberg, A. 243
Semi-simple F-algebra 28
Semisimple element of GL 340
Semisimple Hopf algebra 182 221
Semisimple triangular Hopf algebra 224
Semisolvable 224
Semistandard tableaux 117
Separable algebra 221
Separants 301
Separated ideals 261
Separated in pairs 261
Separated varieties 265
Sergiescu, V. 436
Serre subcategory 26
Set of -generators 246
Set of constants 272
Set of parameters 298
Shape of a Young tableau 113
Sheaf 39
Sheaf on a site 39
Shephard group 364
Shephard — Todd 376
Shephard — Todd, classification 345 347 368
Shephard — Todd, classification for reflection groups 346
Shephard, G.C. 341
Shimakawa, K. 6
Shlepkin, A.K. 488
Shuffling 260
Shunkov group 469
Shunkov problem 470
Shunkov, V.P. 469 475 479 481 484 487—489 491
Sigma-notation 177
Sign character 346 370
Sign map 49
Signature defect 49
Similarity invariant 400 403 410
Simple -ring 246
Simple algebra 81
Simple coalgebra 179
Simple difference ring 246 323
Simple group 387
Simple holonomic 92
Simple Lie algebra 111
Simple Poisson algebra 103
Simple ring 204
Simple root 123
Simple system 356
Simplicial Abelian group 43
Simplicial group 7
Simplicial identity 7
Simplicial object 5 7
Simplicial ring 7 10
Simplicial set 7
Simplicial space 7
Simplicial W-category 21
Simplicity criterion 361
Simplicity of the Chevalley groups 361
Simply connected 12
Singular braid 431
Singular braid, group 450
Singular braid, monoid 450
Singular chain complex 41
Singular component 298
Singular homology 41
Singular realization 301
Sit, W. 243
Site 38
Skew, Gelfand — Tsetlin pattern 136
Skew, group algebra 198
Skew, representations of twisted Yangians 158
Skew, symmetric form 227
Skew-primitive element 180 228
Small category 63
Smallest Hurwitz group 390
Smash coproduct 220
Smash product 193 198 205 228
Solution of a set of -polynomials 253
Solution of a system of -equations 286
Solution of a system of algebraic difference equations 286
Solution of a system of difference algebraic equations 252
Solution, field 316 318
solvable 226
Solvable by elementary operations 321 322
Somewhat commutative algebra 92 100
Sossinsky, A.B. 430 446
Soule Chern character 6 47
Soule etale Chern character 46
Soule, C. 45 46
Sozutov, A.I. 491
Space of regular orbits 444
Span S 64
Specht, E. 373
Special basis 112
Special linear group 44
Special set 292 293
Special value of the zeta function 52
Specialization 293 295
Specialization of a principal realization 300
Spectral decomposition 130
Spectral sequence 14 43 273
Spectrally complete 410
Spectrum 5 7 10
Sphere 389
Sphere, spectrum 11
Spherical triangle 388
Split algebra 37
Split exact 66 67
Splitting field 368
Splitting result 64
Sporadic simple group 361 387
Square free order 60
Stabilizer 36 443
Stable category 23
Stable derived category 5 23
Stable quasi-isomorphism 23
Standard Cartan matrix 351
Standard filtration 81 84 93 272
Standard finite-dimensional filtration 84 95
Standard generator 306
Standard graded algebra 282
Standard p-dimensional filtration 276
Standard ranking 254 257
Standard tableau 114
Statistical mechanics 175
Steenrod algebra 455
Steinberg group 12
Steinberg symbol 34 38
Steinberg theorem 362
Steinberg, R. 342 344 369 403
Stepwise compatibility condition 308
Strength 286
Strength of a system of difference equations 287
Strength of a system of equations in finite differences 286
Strictly real 484
Strings of a braid 431
Strodt, W. 243
Strongly embedded 486
Strongly graded 201
Strongly normal extension 323
Strongly separated 261
Strongly separated in pairs 261
Strongly simple Poisson algebra 103
Structure group 8
Strunkov, S.P. 479
Sub-reflection datum 343
Subcoalgebra 455
Subindexing 291 292
Substitution 251
Suchkova, N.G. 488
Summit set 441
Super Mickelsson—Zhelobenko algebra 136
Superalgebra 215
Superposition of functions 430
Suslin, A.A. 38
Suspension spectrum 11
Swan K-theory 11
Swan — Gersten K-theory 12
Swan, R.G. 5
Sweedler Hopf algebra 183 218 228
Sweedler, M.E. 177
Sylow, 2-subgroup 485
Sylow, p-subgroup 58
Sylow, subgroup 472 476
Sylow, theorem 344
Sylow, theory 344
Sylow, torus 344 345
Sylvester theorem 136
Symbols in arithmetic 34
Symmetric algebra 340
Symmetric bicharacter 190
Symmetric form 227
Symmetric genus 397
Symmetric group 113 345 434 444
Symmetric group, relations 448
Symmetric Martindale ring of quotients 207
Symmetric monoidal category 5 18
Symmetric polynomial 117
Symmetric power 340
Symmetric rigid tensor structure 211
Symmetric structure 210
Symmetrizable 359
Symmetrizable, Cartan matrix 359
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