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Karpilovsky G. — Unit groups of classical rings
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Название: Unit groups of classical ringsАвтор: Karpilovsky G. Аннотация: The subject matter of this book lies at the crossroads of four areas: ring theory, group theory, group representation theory, and algebraic number theory. Like so many interdisciplinary studies, it has its fascinations and attractions, but also its inherent dilemmas. A multitude of concepts and devices pertaining to the structure of groups and rings, algebraic АГ-theory, algebraic and analytic number theory, valuation theory, and group representation theory are used in open or disguised form to investigate the structure of the unit group of a particular ring. This provides for a vivid interplay among, and is a source of enrichment for, the mentioned disciplines. The leitmotif in our discussion is created by the following two related problems.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1988Количество страниц: 370Добавлена в каталог: 11.06.2011Операции: Положить на полку |
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Предметный указатель
Absolute ramification index 120 Absolute residue degree 120 Algebraic algebra 183 Algebraic element 183 Amitsur 199 Apostol 80 Artin 104 227 228 Artin — Rees lemma 227 Associated primes 93 Augmentation 249 Augmentation ideal 249 Augmentation map 249 Ayoub, C. W. 342 Ayoub, R. G. 342 B-high subgroup 157 Baer 98 99 Bass 88 225 233 234 240 242 243 244 Bass independence theorem 88 Bernstein 45 54 Borel 245 Bounded subset 21 Bourbaki 2 21 155 242 111 Brandis 136 144 Brauer 185 Canonical fundamental unit 50 Carin 161 Cartan 185 CHARACTER 74 Character, Dirichlet 76 Character, identity 74 Character, primitive 76 Character, principal 74 Characteristic 2 Chevalley 16 22 Chevalley — Hasse theorem 22 Class group 3 Class number formula 80 Cliff 292 300 305 306 308 Codifferent 136 Cohen 119 Cohn, J. A. 262 Cohn, J. H. E. 54 Cohn, P. M. 2 168 212 Concalves 201 205 206 207 208 210 310 Conductor 76 Congruence subgroup 225 Content 239 Continuons chain of finite extensions 158 Cube-free integer 45 Curtis 276 Dedekind 15 46 79 231 Dedekind domain 3 Dedekind zeta-function 79 Degert 44 delaunay 45 53 54 Dennis 292 Dirichlet 16 24 76 77 175 233 Dirichlet L-function 78 Dirichlet unit theorem 24 Discriminant 6 Discriminant ideal 4 Division ring 179 Eisenstein 128 Elementary matrix 234 Elementary row operation 238 Elementary subgroup 234 Euler function 7 Exponent of Galois extension 151 F-conjugate 322 F-conjugate, characters 322 F-conjugate, classes 322 F-conjugate, idempotents 323 Faddeev 54 Field 5 Field extension 5 Field extension, abelian 154 Field extension, cyclic 6 Field extension, finitely generated 5 Field extension, Galois 6 Field extension, separable 6 Field extension, solvable 154 Field extension, totally ramified 122 Field extension, unramified 122 Field, complete 8 Field, complete discrete valued 112 Field, completion of 8 Field, finitely generated 5 Field, first kind 46 Field, fixed 5 Field, formally real 106 Field, function 102 Field, global 102 Field, imaginary quadratic 34 Field, local 112 Field, p-adic 127 Field, perfect 116 Field, pure cubic 45 Field, rational p-adic 108 Field, real closed 106 Field, real quadratic 34 Field, second kind 46 Field, totally complex 10 Field, totally real 10 First factor 72 Fomin 99 Formal power series 119 Fractional ideal 3 Franz 87 Franz independence lemma 87 Fuchs 11 107 Fundamental system 25 344 Fundamental unit 25 Gauss 77 Gauss sum 77 Gilmer 217 Gilmer's theorem 217 Goncalves — Mandel’s conjecture 206 Gorenstein 307 Group 1 Group algebra 246 Group of type 95 Group ring 246 Group, binary tetrahedral 11 Group, bounded 2 Group, circle 175 Group, cyclic 1 Group, dicyclic 11 Group, dihedral 286 Group, divisible 2 Group, elementary abelian 96 Group, free modulo torsion 1 Group, full rational 95 Group, hamiltonian 268 Group, linear 203 Group, multiplicative 1 Group, p-component of 1 Group, periodic 182 Group, quasi-cyclic 95 Group, quaternion 11 Group, reduced 2 Group, right-ordered 270 Group, splitting 1 Group, torsion 1 Group, torsion-free 1 Group, unique product 269 Group, weakly nilpotent 188 Hall 268 Harish — Chandra 245 Hartley 315 316 Hasse 16 22 123 124 Height 97 Hensel 131 134 Hensel's lemma 9 Herstein 189 198 199 200 205 Herstein’s conjecture 198 Higman 267 268 321 342 hilbert 349 Hilbert’s basis theorem 3 227 Homological dimension 241 Hua 185 Huppert 301 306 Huzurbazar 186 Idempotent 2 Idempotent, orthogonal 2 Idempotent, primitive 2 Idempotent, subalgebra 337 Idempotent, trivial 2 Independent system 20 Inertia field 124 Infinite general linear group 235 Inner automorphism 274 Integral domain 3 Integral element 3 Involution 280 Irreducible component 242 Irreducible topological space 242 Isometric isomorphism 8 Jacobson 101 Jacobson radical 2 Janusz 2 295 Kaplansky 184 345 Karpilovsky 275 276 327 329 330 339 Kneser 146 Krempa 229 232 273 kronecker 15 30 Krull 231 232 243 Krull dimension 243 Krull domain 231 Kulikov 97 Kummer 83 Lang 2 80 81 174 Latimer 28 legendre 40 Legendre symbol 40 Lichtman 206 210 213 Lichtman's conjecture 206 Livingstone 262 Lueroth 143 Malek 228 Mandel 201 205 206 208 210 Matsumura 244 Maximal divisible subgroup 2 Maximal torsion subgroup 1 May 141 149 153 154 156 158 160 161 165 166 167 168 169 173 175 233 318 326 327 332 333 334 337 339 342 Milnor 82 225 343 Minkowski 30 Monastymyi 205 Monomial 247 Multiplicative residue system 112 Nagao 242 Nagell 45 53 54 55 60 Narkiewicz 5 Nil ideal 2 Nilpotent element 2 Nilpotent ideal 2 Nilradical 2 Noether 208 Noether's normalization theorem 230 Noetherian space 242 Non-quadratic residue 40 Norm 4 Norm homomorphism 5 Normalization 189 Normalized group basis 265 Normalized unit 253 Order 119 Outer automorphism group 274 p-rank 97 Passman 256 258 261 263 288 290 Pearson 217 220 Pell's equation 36 Perlis 324 Pickel 315 316 Place 257 Prime element 93 Prime of field 7 Prime subring 2 Principal fractional ideal 3 Product formula 17 Projective map 251 Projective resolution 241 Pruefer 98 Pure subgroup 99 Quadratic residue 40 Quadratic symbol 174 Quaternion algebra 313 Ramachandra 82 Ramification index 4 Ramified prime 4 Rees 227 228 Regular representation 256 Regulator 26 Reiner 276 Relative class number 72 Residue degree 4 Residue system 112 Richaud 44 Riemann 78 Riemann zeta function 78 Right global dimension 242 Ring 1 Ring of p-adic integers 108 Ring, associative 1 Ring, euclidean 238 Ring, finitely generated 2 Ring, primary 215 Ring, projective limit 108 Ring, reduced 2 Ring, semisimple 2 Ring, torsion-free 11 Roggenkamp 292 Roquette 119 231 232 Rossa 274 S-unit 16 S-unit group 16 Saksonov 260 327 Samuel 232 Schenkman 161 Schneider 217 220 schur 204 Scott, W. R. 189 Sehgal 261 279 300 305 306 308 315 Serre 280 Signature 10 Skolem 208 Skolem — Noether theorem 200 smith 263 288 290 Special Whitehead group 238 Square-free integer 31 Square-free part 31 Stender 45 Strojnowski 271 Stuth 195 196 197 Subnormal subgroup 184 Support 247 Supporting subgroup 247 Supporting subring 247 Tits 207 Torsion subgroup 1 Torsion-free rank 97
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