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Yam T.Y. — Lectures on Modules and Rings |
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Предметный указатель |
-unique 473
§18F
(torsion-free) rank 57 242 257
ACC on annihilators 38 229—230 233 243 252—253 262 283 293 324 329 340 420
ACC on complements 217
ACC on direct summands 231
ACC on principal ideals 56 230
Addition complement 214 541
Agnarsson — Amitsur — Robson Theorem 464
Agnarsson, G. x 464 478 479
Albrecht, R. 43
Amitsur, S.A. 383 464 479
Anderson, F.W. 1 534
Ann, P.N. 534
Annin, S. x
Arhangel'skii, A.V. 460
Artin — Rees lemma 105
Artin, E. xvii 105 116 333 365
Artin, M. 201
Artinian module 211 269 507 523 526 529
Artinian radical 333 343 529
Artinian ring 90 105
Artinian ring of quotients §12
Asano, K. 300
Associated prime 86 117 285
Associative pairing 67 438—439 457
Atiyah, M.R. 106 408
Attarchi, H. 345
Auslander's Theorems 184 188
Auslander, M. 16 181 184 187 194 197 201 203
Azumaya's Theorem 485
Azumaya, G. 53 85 163 407 460 485 514 525 533
Baer (or prime) radical xviii 346—351
Baer *-ring 264
Baer ring §D
Baer's Test (or Criterion) 63
Baer, R. xviii 22 63 74—75 80 260—261
Basic ring, basis 492—493 460 502
Bass — Papp Theorem 80—81
Bass' Theorem 187
Bass, H. 20 40 59 144 161 201 204 229 345 415 421 460
Baxter 408
Beachy, J.A. 538
Benson, D. 455
Berberian, S.K. 260 265
Bergman's examples 310—311 330 482 502
Bergman, G.M. x 6 14 294 310 330 331 482 502
Bernstein, S.N. 116
Bezout, E. 305
Bhatwadekar, S.M. 192
Bimodule 37 68 238 312 334 488 513
Bjoerk, J.-E. 113 201
Bjork's example 113
Blackadar, B. 505
Bokut', L.A. 293
Boolean algebra 271 335 338
Boolean ring 65 118 261 381—382
Bourbaki, N. 15 57 122 139 147 527
Bowtell, A.J. 293
Brauer's Equivalence Theorem 446
Brauer, R. 407—408 446 452—453
Brewer, J.W. 42
Buchsbaum, D. 16 194 197 203
Bumby, R.T. 116
Camillo, V.P. 219 329 354 504
Canonical cogenerator 508
Carrier, P. 136
Cartan matrix 430 457
Cartan, E. 430
Cartan, H. 82
Categorical property §18A
Cedo — Herbera example 312
Cedo, R. 312—313
Central closure 395 405
Character module 124 183
Chase's example 47
Chase's Theorems 139 142 146
Chase, S.U. 45 47 112 130 136 139 142 146—147 161
Chatters, A.W. 330 468
Chevalley, C. 102 365
Chihata, C.G. 292 299
Claborn, L. 39
Class number 39
Classical order 322—323
Classical ring 320
Classical ring of quotients §10 299
Closed submodule §6B 218 222 259 262
Cofaithful module 538
Cogenerator (module) 124 507—510
Cogenerator ring §19B 522 524 538—539
Cohen, M. 398
Coherent module/ring §4G
Cohn, P.M. 8 10 11 19 45 116 131 155 294 297—298 300 482
Cohopflan module 17 343
Colby, R.R. 522
Complement §6B 215 243 334
Complete lattice 244 271
Completely CS-module 222
Completion 104 115 120 528
Connell, I.G. 420
Continuous module 227 245—246 361
Costa, D.L. 42
Croisot, R. 287 320 327
CS-module §6D 222 240 243 270
Curtis, C.W. x 450
Davis, E.D. 356
Dedekind domain 38 43 73 476
Dedekind, R. 43 73 476
Dedekind-finite module 18 241 244
Dedekind-finite ring 5 18—19 226 231—232 244
Dense right ideal 338 368
Dense submodule §8
Deuring, M. 115
Dieudonne's theorem 422
Dieudonne, J. 422 527
Dimitric, R. x
Direct limit 19 81 123 134 156
Dischinger, E. 515
Divisible hull 294 309
Divisible module 70 73 96—97
Domain xviii §9B 294 377
Double annihilator condition 100 365 409 511 522 538
Douglas, A.J. 117
Dress, A.W.M. 496
Drisko, A. x
Dual basis lemma §2B
Dual Goldie dimension 213
Dual module 70 97
Duality 515
Dung, N.V. 227
Eakin — Nagata — Eisenbud Theorem 112
Eakin, R. 110 112
Eckmann, B. 74—75
Eilenberg's Trick 22
Eilenberg, S. 22 82 434 443 459
Eisenbud — Robson Theorem 112
Eisenbud, D. x 105 110 112 195 283 419
Emmanouil, I. x 23 153 158 540
Endo, S. 136 270
Equational Criteria for Flatness 130
Essential closure 219—220
Essential submodule 74
Essentially f.g. module 266
Etale algebra 69 541
Euler characteristic 203
Everett, Jr., C.J. 3
Ext-functor 179
Extended centroid 390 405
Extending module 227
Exterior algebra 15 175
| Faith — Walker Theorem 412—413
Faith, C.C. vii ix x 1 82 119 240 283 285 359 413 420 513
Faithful module 52 58 100 481 485 495 538
Faithfully balanced bimodule 488 493 513 521
Faithfully flat extension 151 162
Faithfully flat module §41 162
Farahat, H.K. 117
Farbman, R. x 23
Fieldhouse, D.J. 155 159 163
Findlay, G.D. 207 272 357
Finite representation type 455
Finitely cogenerated (f.cog.) module 506—507 521 537
Finitely generated (f.g.) module 481 501 521
Finitely presented (f.p.) module 57 §4D 156—157
Finitely related (f.r.) module 131
Fisher, J.L. 287 295
Fisher, J.W. 287 339
Flat dimension 183
Flat module §4 318
Flat shift 183
Formanek, E. 113
Fractional ideal 31
Free algebra 14 295—297 305 374
Free module §1
Free resolution 20 170 175 203
Freyd, R. 116
Frobenius algebra 66—69 107 114—115 419 §16C
Frobenius Criterion 451
Frobenius ring §16B
Frobenius, E.G. 66 407—408 §16G 450 453
Fuchs, L. 245
Fuchs, P.R. 479
Full idempotent 485 491—492
Fuller, K.R. 1 522 533 534
Fully divisible module 119
Gabriel's theorem 378
Gabriel, P. 378
Galois duality 516
Galois, E. 516
Gel'fand — Naimark duality 516
Gel'fand, I.M. 516
General right ring of quotients 366 381
Generation Lemma 2
Generator (module) 54 483 503
Gentile, E.R. 476
Giorgiutti, I. 457
Goel, V.K. 239 245
Golden ratio 33
Goldie closure §7C 256
Goldie dimension 209
Goldie's p-rank §1
Goldie's Theorems 304 §11
Goldie, A.W. 207 208 221 253 255—257 287 320 327 339 342 345
Goodearl, K.R. 11 74 136 192 208 354 380 460 476
Gorenstein, D. 408 419
Gorentein rings (0-dim., local) 408 419 421—422
Govorov, V.E. 121 134
Grothendieck, A. 541
Group ring/algebra 69 170 250 323 330 351 442
Gruenberg resolution 20
Gruenberg, K. 20
Guralnick, R.M. 329
Haefner, J. 504
Hajarnavis, C.R. 330
Handelman, D. 11
Harada, M. 227
Hattori — Stallings trace 504
Hattori, A. 504
Herbera, D. 312—313
Herstein, I.N. 8 339
Hilbert basis theorem 15 143 201 232 234
Hilbert space 261 265
Hilbert's syzygy theorem 177
Hilbert, D. 15 143 177 232 234 261 265 295
Hollow module 213
Hopf algebra 408
Hopf, H. 5 408
Hopfian module 5 7 18 115
Hopkins — Levitzki theorem xviii 112 332
Hopkins, C. 112 332 339
Huisgen-Zimmermann, B. x 164 460
Huneke, C. x 105
Hungerford, T.W. ix xviii
Hurwitz, A. 323
Huynh, D.V. 227
Ideal class group 36
Idlaviv, A. 550
Ikeda, M. 365 383
Indecomposable injective §3F 115 212 331
Indecomposable module xviii 84
Injective cogenerator 509—510
Injective dimension §5C
Injective equivalence 178
Injective hull (envelope) 75 §3J 212 331
Injective module §3
Injective Producing Lemma 62
Injective Schanuel's Lemma 178
Injective shift 178
Invariant basis number (IBN) 3 293—294 482 502
Inverse polynomials 107 422
Invertible module 27
Involution 249
Isaacs, I.M. ix xviii
Isaksen, D. x
Jacobson radical xviii 18 49 77 359 362 495
Jacobson semisimple ring xviii 99 376
Jacobson, N. xviii 18 232 365
Jain, S.K. x 227 239 245 377 380—381
Jategaonkar's Lemma 295
Jategaonkar, A.V. 184 295 314
Jensen, C.U. 184
Johnson — Wong Theorem 365
Johnson's Theorem 376
Johnson, R.E. 207 259 272 357 359 365 376
Kaplansky's Theorems 19 42
Kaplansky, I. 8 19 25 42 45 97 165—166 169 171 173 179 202 260—261 265
Kasch, E. 1 242 515 539 540
Kato, T. 538
Kerr's examples 310 328—329
Kerr, J.W. 310 328—329
Kharchenko, V.K. 388 396 398
Kirkman, E. x
Klein, A.A. 18 293—294
Koenig, D. 232
Koszul algebra 408
Koszul resolution 175 202
Koszul, J.-L. 175 202 408
Kothe, G. 495
Krull dimension 194 200 321
Krull's intersection theorem 117
Krull, W. 85 117 197 287
Lam, C.K. vx
Lam, T.Y. x 38 55 177 201 285 300 321 343 380 450 467 478
Lambek's Theorem 125
Lambek, J. ix 74 124—125 207 208 272 335 357
Lang, S. ix xviii
Lanski, C. 339
Lasker — Noether Theorem 102 117
Lasker, E. 102
Lawrence, J. 249 418
Lazard — Govorov Theorem 134
Lazard, M. 121 134
Lefshetz, S. 527
Left coherent ring 138—139
Lenagan's Theorem 332
Lenagan, T.H. 332—333
Lenstra, Jr., H.W. x 28 36 39
Leptin, H. 541
Leroy, A. x 380 467
Lesieur, L. 287 320 327
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