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| Lam T.Y. — A first course in noncommutative ring theory |
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| Предметный указатель |
 6 140
 140—141 148
 90
 , octahedral representation 148
 129 146 149
 139—140 148
 -conjugacy class 187
-conjugate 187
-ideal 44
-simple ring 44
 97
 105
 -potent element 156 157
 -potent group 156
 -conjugacy class 189
-conjugate 189
-derivation 12
-ideal 44
(Multiplicative) commutator 214 221—222
Abelian Lie algebra 13
Absolutely irreducible module 111
Absolutely simple module 111
ACC on annihilators 175
ACC on ideals 180 337
ACC on principal right ideals 355
Additive category 15
Additive commutator 115 214 216 261
Adjan, S.I. 150
Adjoint of an operator 174
Affine algebra 72 73
Akizuki — Cohen Theorem 350
Akizuki, Y. 350 351
Albert — Neumann — Fuchs Theorem, 281
Albert's Theorem 290
Albert, A.A. 220 259 281 290
Algebra of quantum mechanics 7
Algebraic algebra 63 219 226 257
Algebraic element 25 62
Algebraic K-theory 313 314 316 377
Algebraically closed division ring, 269—271
Amitsur — McCoy Theorem 171
Amitsur's Theorems 45 63 75 77 92 216
Amitsur, S.A. xiii 45 63 75 77 85 86 92 104 171 181 216 226 381
Annihilator (left, right) 49 53 175 179 202
Archimedean class 245 292
Archimedean ordered group 105
Archimedes 105 245 282 284 292
Artin — Schreier Theorems 255 256 277
Artin — Whaples Theorem 201
Artin, E. vii 1 21 26 31 35 51 58 201 248 255 275 277 279 284
Artinian module 20
Ascending chain condition (acc) 1 20
Atiyah, M.F. 2 302
Augmentation ideal 85 131 211
Augmentation map 84
Auslander, M. 123
Axchimedean ordered ring 282—283
Axtinian ring 20
Azumaya, G. 64 301 302
Baer — McCoy radical 168
Baer's lower nilradical 168
Baer's Theorem 270
Baer, g. 168 270
Banach algebra 85—86 90
Banach, S. 85
Basic idempotent 372
Basic ring 372
Basic ring (of a ring) 372
Basic semiperfect ring 375
Bass' Theorems 313 354 369
Bass, H. 313 335 358 369
Bergman's examples 182 335
Bergman's Theorem (on graded Rings) 82
Bergman, G.M. 75 82 182 335
Berman's Theorem 144
Betman, S.D. 144
Bimodule 17
Binary tetrahedral group 6 215
Birkhoff — Iwasawa — Neumann Theorem 102
Birkhoff — Vandiver Theorem 215
Birkhoff's theorem 205
Birkhoff, G. 13 102 205
Birkhoff, G.D. 215
Bjoerk's Theorem 355 357
Bjoerk, J.E. 355 357
Blackburn, N. 103
Block decomposition 337
Boole, G. 212 343
Boolean ring 212 343
Brauer group vii viii
Brauer — Albert Theorem 259
Brauer — Nesbitt — Nakayama Theorem 377
Brauer — Thrall Conjecture 123
Brauer's example 236
Brauer's Lemma 172
Brauer's Theorems 126 132 226
Brauer, R. vii 123 126 132 172 220 222 224 226 236 259 377
Braun, A. 176
Bray — Whaples Theorem 268
Bray, U. 268
Brown, B. 68
Brown-McCoy radical 68
Brungs, H.H. 309
Burnside's Lemma 109
Burnside's Problems 150
Burnside's theorems 151 152
Burnside, W. 108 109 150 151 152
C*-algebra 90
Cancellation Theorem (for modules) 315
Cartan matrix 376—380
Cartan — Brauer — Hua Theorem 222 226
Cartan, E. 51 346 376
Cartan, H. 222
Cassels' Theorem 290
Cassels, J.W.S. 290
Cauchy's theorem 84 92
Cauchy, A. 84 92 330
Center 48 49 124 228—229
Center of a group ring 134
Center of a left primitive ring 195 201
Central idempotents 24 135 319 336 343
Central multiplicative set 77
Central simple algebra viii 214
Central units (in group rings) 142
Centralizer of a set 214
Centrally finite division ring 213 228—229
Centrally infinite division ring 213 228—229 247
Centrally primitive idempotent 336
Change of rings  5
CHARACTER 117
Character table 139
Chevalley, C. 182 191
Class function 136
Clifford algebra 13
Clifford's theorem 130 160
Clifford, A.H. 130
Clifford, W.K. 13
Cohen, I.S. 306 350
Cohn's examples 248
Cohn, P.M. 247 248 274 318 381
Cohomology of rings vii
Coleman, D.B. 147
Column rank (of a matrix) 227
Commutator subgroup 96
Complementary idempotent 318
Completely (or strongly) prime ideal, 2O6
Completely primary ring 301
Completely reducible (or semisimple) module 26
Completely reducible linear group, 154
Composition series 20
| Convolution 90
Cormell, I.G. 92 170
Countably generated algebra 64
Cozzens, J.H. 42 381
Crossed product 247
Curtis, C.W. 126 142 149 381
Cyclic algebra 220 229
Cyclic division algebra 232 233 238—239 241
Cyclic module 29 53
Cyclotomic polynomial 127 215
Dade's Lemma 342
Dade, E.C. 342
Dauns, J. 247 381
DCC on ideals 337
DCC on principal left ideals 173 354 355
DCC un finitely generated submodules 354
Dedekind cut 283
Dedekind domain 302 305
Dedekind, R. 4 283 302
Dedekind-finite ring 4 24 25 49 67 295 313 314 316 328
Dense ring 190
Dense set of linear operators 192
Density theorem 191—193 252
Derivation 11
Descending chain condition (OCC) 1 20 241
Deuring, M. 304
Diagonalizable operator 42
DickSOh'S Theorems 265 308
Dickson's example 238
Dickson, L.E. 83 125 228 29 233 238 248 265 308 381
Dietzmann's Lemma 105
Dietzmann, A.P. 105 170
Dieudonne's example 23
Dieudonne, J. 23
Differential operator vii 7
Differential polynomial ring 11 12 44—45 62 187
Dihedral group (finite) 148
Dihedral group (infinite) 94 97 105
Dirac, P.A.M. 7
Direct product of rings 24
Divinsky, N.J. 176 206
Division closure of a preordering, 279
Division rings 1 4 9 Chapter
Division-closed preordering 280
Domain 3
Double centralizer property 39 50
Double centralizer theorem 254 261
Eagon, J.A. 73 381
Emmanuel, J. 124
Entire function 89
Enveloping algebra vii 13
Equivalent representations 83
Euclid 23 187 262
Euclidean algorithm 23 187 262
Extendibility of an ordering 280
Exterior algebra 13 60 297
Faith, C. 42 223 224 381
Faithful semisimpie module 182
Faithful simple module 182 188—189 201
Feit, W. 142
Fermat's little theorem 115
Fermat, P. de 115
Finite conjugate (Lc.) group 97
Finite representation type 123
Finite-dimensional algebras 108
Finitely generated algebra vii 71—72 176 332
Finitely presented module 124
Fitting Decomposition Theorem 299
Fitting, H. 299
Flat module 365
Formal power series ring 9
Formal reality 91 277
Formally real ring 91 279 290—291
Formanek's Theorem 198
Formanek, E. 94 198
Fourier exansion 146
Free group 102
Free k-ring 6 196—197 247 283
Free product of semigroups 198
Frobenius' Theorem 219 256
Frobenius, F.G. 82 136 219
Fuchs, L. 275 281 381
Full idempotent 322
Gabriel, P. 302
Galois, E. 80 229 231 240
Generators and relations 7
Gerstenhaber — Yang Theorem, 256
Gerstenhaber, M. 256 382
Goldie's Theorem viii
Goldie, A.W. viii 22
Golod, E.S. 150
Gordon — Motzkin Theorems 263 266
Gordon, B. 263 266
Graded ideal 82
Graded ring 82 238
Graetzer, G. 282
Green, J.A. 146
Grothendieck groups vii 377
Grothendieck, A. vii 377
Group character 117 125
Group representations 83 Chapter
Group ring 8
Haar, A. 90
Hahn, H. 228 241
Hall, Jr., M. 150
Hamilton, W.R. 5 220
Hasse, H. 220
Heisenberg Lie algebra 14
Heisenberg, W. 14
Herstein — Kaplansky Theorem, 210
Herstein's Conjecture 222
Herstein's Lemma 217
Herstein's Theorem 225
Herstein, I.N. 85 104 180 209 210 213 217 222 225 257 382
Higman's theorem 142 144
Higman, G. 142 144
Hilbert basis theorem 23
Hilbert domain 71
Hilbert ring 71—72
Hilbert space 174
Hilbert's 17th problem 279
Hilbert's example 288
Hilbert's Nullstellensatz 60 72 73
Hilbert's twist 10
Hilbert, D. 10 11 23 60 71 174 228 229 241 279 282 286 288
Hirsch, K.A. 50
Hoelder's Theorem 105
Hoelder, O. 34 105 304
Hoffmann, D. ix
Homological algebra vii
Hopkins — Levitzki theorem 21 32 59
Hopkins, C. 21 32 59
Hua, L.K. 222 223 260
Humphreys, J.E. 161
Huppert, B. 103
Hurwitz' ring of quaternions 6
Hurwitz, A. 6
I-adic completion 330
I-adically complete 330
Icosahedral representations 142
icosahedron 141
Ideal 3 19
Ideals in matrix rings 32
Idempotent 24 145
Idempotent ideal 181
Idempotents in integral group rings 145 335
Indecomposable module 119 120—123 298
Indecomposable ring 336
Infinite representation type 123
Infinitely large element 282
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