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| Lam T.Y. — A first course in noncommutative ring theory |
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| Предметный указатель |
Infinitely small element 282
Injectire module 30
Inner derivation 12 216
Inner order 46
Inseparable element 81 274
Integral domain 3
Integral group ring 8
Integral Quaternions 6
Invariant theory vii
Invariant valuation ring 310
Inverse 4
Invertible 4
Involution 87 91
Irreducible linear group 161
Irreducible module 26
Irreducible representation 83
Isaacs, I.M. 142 382
Isomorphic idempotents 326
Ito, N. 139
Iwa.sawa, K. 102
J-semisimple ring (or semiprimitive ring) 34
J-semisimplicity Problem ix
Jacobson radical 21 52 53
Jacobson — Azumaya 64
Jacobson — Chevalley Density Theorem 191
Jacobson — Herstein Theorem 209
Jacobson's example 328
Jacobson's Theorems 209 219 226 261
Jacobson, N. vii 32 41 52 53 64 85 164 176 182 191 195 201 209 213 219 226 240 255 257 259 261 269 273 356 382
Jacobson-semisimple ring 52 55 57 62 68 71 86 92—94 101 102 105 182
Jategaonkar's examples 182
Jategaonkar, A.V. 182
Johnson's Theorem 279
Johnson, R.E. 275 279
Jonah's Theorem 355
Jonah, D. 355
Jordan canonical form 120
Jordan — Hoelder theorem 34 36 38
Jordan, C. 34 120 304
Jordan, D.A. 46 382
Jordan, P. 7
Kaplansky's Theorem 307
Kaplansky, I. 2 25 147 153 195 210 213 258 260 307
Karrass, A. 103
Killing form 51
Killing, W.K.J. 51
Klein 4-group 146
Koethe's Conjecture ix 77 174 176 181
Koethe, G. ix 77 174 181 247
Kolchin's Theorem 160
Kolchin, E.R. 108 157 160
Krempa, J. 181
Kronecker's Rank Theorem 227
Kronecker, L. 135 227
Krull valuation 249 291 309
Krull — Azumaya 64
Krull — Schmidt decomposition, 294 301
Krull — Schmidt theorem 303 332
Krull — Schmidt — Azumaya Theorem 302
Krull's theorem 310
Krull, W. 64 249 291 293 296 301 302 310
Kummer, E. 249
Lain, T.Y. 273 289 290 382
Laurent polynomial ring 11 95
Laurent series ring 9 243
Laurent, H. 9 11 228 241
Left algebraically closed 269
Left Artinian ring 20
Left dimension 248
Left Goldie ring 22
Left ideal 3 18
Left identity 25
Left inverse 4 24 25
Left irreducible idempotent 323
Left Noetherian ring 20
Left operator 33
Left perfect ring 353
Left polynomial 10
Left primitive ideal 183
Left primitive ring 41 163 182 198
Left quasi-regular 67
Left stable range 1 314
Left T-nilpotent set 351
Left zero-divisor 3 10
Left-invertible 4 24 53 54 55
Leroy, A. ix
Leung's example 292
Leung's Theorem 292
Leung, K.H. ix 292
Level of a division ring 289
Levi, F.W. 102
Levitzki radical 52 163 177
Levitzki — Herstein Theorem, 180
Levitzki's Theorems 102 176
Levitzki, J. 21 32 52 59 163 173 176 177 180
Lexicographic ordering 102
Lie algebra 13 51
Lie bracket (or Lie product) 13 115
Lie ideal 216
Lie — Kolchin — Suprunenko Theorem, 157
Lie, S. vii 13 51 108 156 157 216
Lifting idempotents 326 329 330
Lifting pairwise orthogonal idempotents 328
Linear group 149
Linkage of primitive idempotents, 337 372
Little ideal 204
Littlewood's formula 149
Littlewood, D.E. 7 149
Local group ring 309
Local idempotent 312
Local ring 13 295
localization 81 294 297
Locally compact group 90
Locally finite group 104 154
Locally nilpotent (one-sided) ideal, 176—177
Locally nilpotent set 176
Logarithmic derivative 187
Lower central series 158
Lower nilradical (or prime radical) 163 164 168
m-system 166
m-transitive 192 194
MacDonald, I.G. 2
Magnus, W. 103
Maguus-Witt Theorem 103
Mal'cev — Neumann construction, ix 241—242
Mal'cev — Neumann — Moufang Theorem 247
Mal'cev, A.I. ix 228 241 247 286
Mal'cev-Neumann ring 242
Maschke's Theorem 83 91 104 146 155
Maschke, H. 83 85
Matrix ring 32 33 49 61 172 181 323 356
Matrix units 33 61 328 335
Maximal ideal 68 165 179
Maximal left or right ideal 53 294
Maximal preordering 278
Maximal subfield 230 248—249 254—255
May, M.K. ix
McCoy's Theorems 180
McCoy, N.H. 68 165 171 180 206
Metro equation 274
Minimal idempotent 333
Minimal left ideal 25 35 38 148 172 185 202
Minimal polynomial 42 264 265 272 274
Minimal prime ideal 180 207
Modular left ideal 68
Modular representation 125
Molien, T. 41 51 125
Monogenic algebra 72
Moore, E.H. 214
Morita Theory 323 370 375
| Morita, K. 41 323 375
Motzkin, T.S. 263 266
Moufang, R. 247
n-abelian group 96
n-system 167
Nagata, M. 64 382
Nakayama's lemma 64 352
Nakayama, T. 64 377
Nathanson, M.B. 179
Nazarova, L.A. 123
Nesbitt, C.J. 377
Neumann's Lemma 97
Neumann's Theorem 105
Neumann, B.H. ix 97 102 105 228 241 247 281 286 382
Neumann, J. von viii 4 65 211
Newton's law 7
Newton, I. 7
Nil (left or right) ideal 91—92 173—176
Nil ideal 52 56 105 181
Nilpotent (left or right) ideal, 52 56 169
Nilpotent group (of class r) 158 223
Nilradical of a commutative ring 60 70 1(}4
Niven — Jacobson Theorem 269
Niven's Theorems 271 272
Niven, I. 269 271 272 382
Noether — Deuring Theorem 304
Noether — Jacobson Theorem, 257
Noether, E. viii 1 21 32 82 107 124 220 247 257 304 382
Noetherian module 20
Noetherian ring viii 20
Noetherian simple ring 46
Non-sociative ring 51
Nontrivial idempotent 293
Nontrivial unit (in group rings) 94 147
Norm 231
Novikov, P.S. 150
Operator algebras vii 174
Opposite ring 5 252
Ordered division ring 285
Ordered group 100 103 242 249 283 287
Ordereft ring ix 276
Ordering of a ring 276
Ore, O. 12 247
Orthogonal idempotents 320
Orthogonality relations 136
Osima, M. 375
Osofsky, B.L. 30
p'-group 92 93 101
p-adic integers 297 299
p-adic numbers 297
p-group 104 122 129 157 131 138 150 298
p-regular conjugacy class 132
p-regular element 132
Palais, R.S. 220
Passman's Theorems 93 105
Passman, D.S. 75 86 90 92 93 98 103 105 170 382
Peirce decomposition 318
Peiree, C.S. 318
Perfect commutative ring 357
Perfect field 113
Perfect ring 353
Pfister's Theorem 289
Pfister, A. 289
PI-algebra 176
Piekerr, G. 275 286
Pierce, R.S. 123 382
Plancherel formula 147
Planeherel, M. 147
Poincare — Birkhoff — Witt Theorem, 13
Poineare, H. 13
Positive cone 100 276
Preordering of a ring 277
Prime group ring 170
Prime ideal 164 165
Prime matrix ring 172
Prime polynomial ring 171
Prime radical (or lower nilradical) 163 164 168
Prime ring 163 168
Primitive idempotent 320
Principal indecomposable module, 308 371
Principal left ideal domain 23
Projective cover 361
Projective module 29 145 307 353 360
Projective space 224 267
Pseudo-inverse 66
Quadratic form 13
Quasi-regular 67
Quaternion algebra (generalized) 232 238 256
Quaternion group 5 6 127 146 148
Quaternions 5 16 25 219 230 269—270
Quebbermann, H.-G. 50
Quotient ring 3 7
Radical ideal 164
Radical of a module 358—360
Radical of an ideal 164 166 168
Radical ring extension 255
Ram's example 178—179
Ram, J. 178
Rank of a free module 49
Rank of a linear operator 50 202
Rational quaternions 5 128
Real-closed field 91 220 255—256 270—271
Reduced ideal 208
Reduced norm 236
Reduced ring 4 71 163
Reductive group 161
Regular one-sided ideal 68
Reiner, I. 126 142 149 381
Relatively archimedean 245
Remainder theorem 262
Remak, R. 302
Rentschief, R. 370
Representations 83 Chapter
Resolvent function 90
Resolvent set 90
Rickart's Theorem 85—86
Rickart, C.E. 85 86 90 382
Rieffel's proof (of the double centralizer property) 39
Rieffel, M.A. 39
Riemann surface 297
Riemann, G.F.B. 297
Right algebraic 272
Right algebraically closed 269
Right Artinian ring 20
Right dimension 248
Right discrete valuation ring, 309
Right Goldie ring 22
Right hereditary ring 378
Right ideal 3 18
Right identity 25
Right inverse 4 24 25
Right irreducible idempotent, 323
Right Noetherian ring 20
Right operator 33
Right perfect ring 58 353
Right polynomial 10
Right primitive ideal 183
Right primitive ring 182
Right quasi-regular 67
Right root 262
Right T-nilpotent set 351
Right zero-divisor 3 10
Right-invertible 4 24
Ring 2
Ring of differential operators 7
Ring of quotients viii 247 281
Ring with involution 87 91
Ring with polynomial identity viii
Ring without identity 24 25 67—68 180 281—282
Ringel, C.M. 123
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