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Hazewinkel M. (ed.) — Handbook of Algebra, Volume 4
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Название: Handbook of Algebra, Volume 4Автор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 518Добавлена в каталог: 30.06.2008Операции: Положить на полку |
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Normal subgroup 187 Normalized generator 125 140 Novikov — Adian group 472 480 Novikov, P.S. 479 487 Null homotopic 25 Nullstellensatz for difference fields 265 Number field 6 33 49 Number of normal orderings 123 ob 64 Ol’shanskii group 480 Ol’shanskii monster 484 Ol’shanskii, A.Yu. 479 Operad of rooted trees 230 Opposite algebra 199 Opposite smash product 205 Orbit category 63 Order 256 271 296 Order of a 296 Order of a 268 Order of a 296 Order of a 272 Order of a difference kernel with respect to an indexing 292 Order of a term 254 256 Order of a variety 297 Order of an ideal 297 Order of unipotency 227 Order, filtration 86 Order, in an algebra 29 Ordered group 441 Ordered monomial 114 Orderly ranking 254 Orderly ranking of 257 Orderly ranking of a set of 257 Ordinary 244 Ordinary character 409 Ordinary difference field 245 261 296 Ordinary difference field, extension 306 Ordinary difference ring 244 Ordinary inversive difference field 291 Ore extension 104 Ore ring 272 Ore subset 100 Oriented n-link 366 Orthant 256 Orthogonal group 401 407 Orthogonal Lie algebra 111 112 116 158 164 Orthogonal twisted Yangian 150 Orthogonality property 116 Orthogonality relations 223 Ostylovskii, A.N. 479 488 p-Adic field 6 27 p-adic group 361 p-adic integers 377 p-adic reflection group 375 p-biprimitively finite 469 p-center 479 p-compact group 376 p-complete topological space 376 p-completion 376 p-dimensional filtration 276 p-minimality condition 473 487 p-real element 491 p-real relating 491 p-regular partition 373 Pairing of exact categories 65 Parabolic subgroup 342 347 370 Partial 244 Partial difference field 288 294 Partial difference kernels 295 Partial difference ring 244 Partially ordered group 312 Partition 370 Partitive algebra 86 89 100 Pathological 311 Pathological difference field extension 311 Paton, M. 430 442 Pattern 134 Pattern calculus 136 Perfect 397 403 Perfect 259 Perfect closure 260 Perfect complex 5 23 Perfect difference ideal 260 261 Perfect group 397 404 Periodic almost locally soluble group 473 Periodic binary soluble group 473 Periodic difference ring 302 Periodic element 302 Periodic group 469 472—474 Periodic part 474 481 Permitted difference field 267 Permitted difference ring 267 Permitted function 267 Permutation conjugacy 449 Permutation representations of T(2,3,7) 415 Permutational representation 391 392 Permutational representation of T(2, 3,7) 387 Perturbative renormalization 230 Picard group 19 40 49 Picard — Vessiot extension 316 Picard — Vessiot ring 323 324 Picard — Vessiot theory 315 Pieri rule 130 Planar graph 436 Poincare series 454 Poincare-polynomial 341 Pointed coalgebra 179 228 Pointed Hopf algebra 182 207 227 Pointwise stabiliser 342 Poisson, algebra 80 102 Poisson, bracket 102 Poisson, matrix 104 Poisson, polynomial algebra 102 103 Polovitskii, Ya.D. 478—480 488 Polyhedral group 389 Polynomial growth 80 Polynomial order 343 Polynomial ring of invariants 375 Positive presentation 447 Positive root 159 161 356 Positive root of maximal height 357 Positively equal 438 Positively graded 268 Power 440 Presentation 429 Presentation of a braid group 429 436 Presentation of the pure braid group 437 Presheaf 39 Primary 295 306 Primary 307 314 Primary finitely generated 314 Primary minimality condition 473 479 Primary thin direct product 477 Prime 245 Prime 245 252 286 Prime algebra 207 Prime difference ideal 245 Prime inversive difference ideal 252 Prime reflexive 261 Prime ring 200 Prime system of 286 Prime system of algebraic 286 Primitive bireflection group 374 Primitive element 180 Primitive group 347 Primitive reflection group 346 Principal component 298 299 Principal realization 293 295 Principal series unipotent character 343 Problem of minimality 487 Product order 278 Profinite G-theory 62 Profinite group 36 37 40 Profinite group, action 65 Profinite higher K-theory 5 62 Profinite K-theory 17 62 Profinite K-theory of orders 6 Projective curve 45 Projective dimension 29 Projective normalizer 347 Projective representation 225 Projective representation of T(2, 3, 7) 405 Projective unitary groups over rings of algebraic integers 410 Prolongation 291 294 Prolongation of difference kernel 291 Proper, 264 Proper, monadic algebraic difference extensions 317 Proper, specialization 293 295 Proper, transform 256 Properly monadic 310 Property 294 Property 294 Property 294 Pseudo-cocycle 192 Pseudo-reflection 340 Pseudo-twist 223 Pseudo-unitary group 137 Pure braid 432 Pure braid, group 362 364 429 434 437 454 Pure braid, group of the action of W on Y 444 Purely inseparable 294 Purely transcendental 375 Purity of the branch locus 341 Pushin, O. 6 51 Pushout 20 PVE 316 PVR 324 Q-L conjecture 48 q-Schur algebra 373 q-special basis 112 qLE 322 QLF-group 476 QSE-group 477 Quantized coordinate algebra 194 Quantized enveloping algebra 115 136 228 Quantum, affine algebra 137 Quantum, algebra 112 136 Quantum, commutative 215 Quantum, determinant 126 148 Quantum, dimension 211 Quantum, double 226 Quantum, fieldtheory 175 212 231 Quantum, Gelfand — Tsetlin module 137 Quantum, group 115 136 176 208 228 Quantum, groupoid 231 Quantum, Lie superalgebra 137 Quantum, Mickelsson — Zhelobenko algebra 136 Quantum, minor 112 133 134 164 Quantum, minor, formula 116 Quantum, plane 215 Quantum, Sylvester theorem 136 Quantum, Yang — Baxter equation 176 208 Quasi-cyclic 2-group 486 Quasi-cyclic group 487 Quasi-cyclic p-group 480 Quasi-determinant 136 Quasi-dihedral group 486 Quasi-exponent 227 230 Quasi-Hopf algebra 177 Quasi-isomorphic 23 Quasi-isomorphism 23 58 Quasi-linearly disjoint 249 294 Quasitriangular 213 217 220 Quasitriangular Hopf algebra 188 210 214 Quaternion 374 411 Quaternion, algebra 410 412 Quaternion, F-algebra 6 61 Quaternion, group 6 58 192 481 Quaternion, norm 411 Quaternionic reflection group 374 Quillen K-theory 5 11 Quillen lemma 101 Quillen plus construction 11 Quillen, D. 5 44 64 Quillen-Lichtenbaum conjecture 6 48 Quotient, 250 252 Quotient, difference field 250 Quotient, division ring 97 Quotient, field 250 r-form 192 R-matrix 136 191 226 R-order 29 55 R-order in a semisimple F-algebra 55 Radford, D.E. 190 Radical 262 Radical of a difference ideal 248 Raising operator 112 116 120 125 131 132 Raising weights 140 Rank 278 ranking 254 256 Rational cohomology 44 Rational equivalence 43 Rational representation 370 Rationally complete 208 Raudenbush, H. 243 RC module 63 Real embedding 49 Real number field 36 Real place 35 Real reflection group 340 343 347 349 363 Realization 293 295 Realization of a difference kernel 293 295 Realization of a symmetrizable Cartan matrix 359 Reduced 257 Reduced 255 Reduced 248 Reduced algebraic subset 325 Reduced decomposition 123 Reduced degree 292 Reduced degree of a difference kernel 292 Reduced element 277 Reduced expression 350 Reduced limit degree 287 Reduced subset 325 Reduced with respect to 255 Reducible 264 Reducible subgroup 403 Reducible variety 264 Reduction of a 257 Reduction, 159 Reduction, 160 Reduction, modulo an autoreduced set 255 Reduction, problem 112 Reduction, process 255 Reduction, theorem 255 Reductive algebraic group 361 Reductive group 343 Ree group 397 Reflecting hyperplane 340 363 Reflection 340 444 Reflection, datum 343 Reflection, group 340 365 368 374 Reflection, group over field of positive characteristic 374 Reflection, over the quaternions 374 Reflection, representation 343 368 369 376 Reflection, subgroup 343 346 Reflexive 245 246 Reflexive closure 246 262 Reflexive prime 298 Reflexive prime ideal 259
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