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Lam T.Y. — A first course in noncommutative ring theory
Lam T.Y. — A first course in noncommutative ring theory

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Название: A first course in noncommutative ring theory

Автор: Lam T.Y.

Аннотация:

By aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation, the author has produced a text that is suitable for a one-semester graduate course or for self-study.


Язык: en

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 209

Добавлена в каталог: 05.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_4$      6 140
$A_5$      140—141 148
$L^1(G)$      90
$O_p(G)$, octahedral representation      148
$S_3$      129 146 149
$S_4$      139—140 148
$\delta$-conjugacy class      187
$\delta$-conjugate      187
$\delta$-ideal      44
$\delta$-simple ring      44
$\delta(G)$      97
$\Delta^+(G)$      105
$\lambda$-potent element      156 157
$\Lambda$-potent group      156
$\sigma$-conjugacy class      189
$\sigma$-conjugate      189
$\sigma$-derivation      12
$\sigma$-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      $\S$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
1 2 3
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