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| Yam T.Y. — Lectures on Modules and Rings |
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| Предметный указатель |
Leung, K.H. x
Levasseur, T. 201
Levitzki, J. 112 332 339
Li, M.S. 372
Linearly compact (l.c.) module 527—529
Linearly compact ring 528
Local Frobenius algebra §15D 421—422 453
Local ring xviii 84 100 104 §5F 418—419 421—422 453—454 526
Localization of injectives 319—320
Localization of Kasch rings 285—286
Locally free module 57
Locally split 163
Loewy series 346
Loewy, A. 346
Lopez-Permouth, S.R. 227
Ludgate, A.T. 314
Macaulay, F.S. 107
MacDonald, I.G. 106
MacLane, S. 459
Maison, C.J. 479
Mal'cev's Theorems 291—292
Mal'cev, A.I. 287 290—293
Malcolmson, P. 8
Marks, G. x
Martindale III, W.S. 357 383 404
Martindale ring of quotients §14 385
Maschke's Theorem xviii 329
Maschke, H. xviii 329
Matlis duality 526
Matlis — Papp — Faith — Walker Theorem 82
Matlis' Theorems 89 104 526
Matlis' Theory §31 104
Matlis, E. 82 89—90 104 114 460 526 537
Matrix units 461—462
Matsumura, H. 113 151
Maximal ring of quotients §13 366
McConnell, J.C. 45 74
McCoy rank 16
McCoy, N.H. 16 195
Meet-irreducible 84 120 331 421
Menal, P. 313
Mewborn — Winton Theorem 252
Mewborn, A.C. 252
Minimal prime 117 330—331 335—337 343 351—352
Modified Flatness Test 125
Modified Injectivity Test 63 72
Modified Projectivity Test 56 63 72
Module category equivalence §17B
Mohamed, S.H. 227 361
Montgomery, M.S. x 8 18 19 396 398
Morita context §18C
Morita dualities §19D 520
Morita equivalent rings 472 482 491—492 504
Morita I, II (for dualities) 520—521 534
Morita I, II, III (for equivalences) §18D
Morita invariant property 482 492 501—502
Morita ring 503
Morita theory (duality) 1 117 §19
Morita theory (equivalence) 1 51 54 232 267 329 §18
Morita's characterization of generators 503
Morita, K. 1 51 54 117 232 267 329 459—460 503 525 533
Moulton, D. x
Mueller, B.J. 53 227 361 460 525 527 529 531—532 534
Mueller, W. 515
Muller's Theorems 531—532
Murray, F.J. 5
Murray, W. x
N-cancellation 474
Nagao, H. 92
Nagata's example 200
Nagata, M. 110 112 143 200—201
Naimark, M.A. 516
Nakayama automorphism §16E
Nakayama permutation §16A 426
Nakayama's example 429
Nakayama, T. 92 365 383 407 417 420 422 426 429 434 437 443 445 453 456—457
Neanderthal, X. x
Nesbitt, C. 407 445 453 456—457
Neumann, B.H. 293
Neumann, J. von xviii 5 265
Nguyen, N. x
Nicholson, W.K. 70 119 382
Noether, E. 101—102 118 115 287 300
Noether, M. 102
Noetherian module 14 118 211 523 526
Noetherian ring 89 102 105—106 §5G 332—333 §12C
Nonsingular module 247 259 269 501
Normal closure 395
Normalizing element 394
Northcott, D.G. 105
Ojanguren, M. 55
Onodera's Theorem 531
Onodera, T. 460 525 527 529 531
Ore condition 303
Ore localization 287 299 318
Ore, O. 287 300 303
Osima, M. 460
Osofsky — Smith Theorem 223
Osofsky's examples 79—80 197 371 514
Osofsky, B.L. x 79 80 114 197 204 223—224 249 285 359 509 514—515 523 539 540
Papp, Z. 80 82
Paratrophic matrix 451
Pascaud, J. 457
Passman, D.S. 324 388 392 401—403
PI-algebra 305
Picard group §2D 203 476
Picard, C.E. 34
Pilz, G.F. 479
Pontryagin duality 516
Pontryagin, L.S. 516
Poonen, B. x
Priifer's Theorem 115
Priifer, H. 66 103 115 128 146 163
Primary decomposition 117—118
Primary ideal 117 353
Prime avoidance 195 283 339
Prime ideal xviii 85 88 315 331
Prime module 85
Prime radical xviii
Prime ring xviii 316 327 330 495
Principal indecomposable 79 92 423—425 428—429
Principal right ideal domain (PRID) 43 65 294 472
Principally injective module 70
Procesi, C. 344
Progenerator 54 473 484
Projection 264
Projective cover 76 540
Projective dimension 168
Projective equivalence 167
Projective module §2
Prufer domain 43 128 146 222 268
Prufer p-group 76 103 276
Pseudo-Frobenius (PF) ring 365 514
Pure exact sequence §4J 162
Pure submodule 153 162—164 243
QF-ring duality 517
QI (quasi-injective) module §6G §13A
QI-envelope 239
Quasi-continuous module 245—246
Quasi-Frobenius (QF) algebra 432
Quasi-Frobenius (QF) ring 365 §15 409 511
Quaternions 323 468—470 479
Quillen, D. 38 177 492
Radical of a module 99 161 537
Rank condition 9 18—19
Rational extension 272
Rational hull §8B 276
Rationally complete module 277—279
Ravel, J. 244
Reduced rank §7C 327
| Reduced ring xviii 59 249 338 344 377 404
Rees, D. 105
Reflexive module 144 413 519—522 526
Regular element xviii 30 325—326 336 348—351 356
Regular local ring 195
Regular sequence 174 202
Reiner, I. 45 450
Renault, G. 324 359
Reznick's anagram 300
Reznick, B. 300
Rickart, C.E. 260
Right Artinian ring 5 49 88 90 322 457 507 533 540
Right Bezout domain 305
Right denominator set 300 317
Right fir 45
Right global dimension 168
Right Goldie ring §11 324
Right hereditary ring 42 49—50 72 124 169 188 §7E 350
Right Kasch ring 189 §8C 280 371 423 511 514 539
Right maximal ring of quotients §13
Right Noetherian ring 7 81—82 120 132 184 194 304 349
Right nonsingular ring 247 262 266 275 324 362
Right order 304 320
Right Ore ring/domain 13 266 303—305 308 310—313 342
Right perfect ring 187 229—230 321 540—541
Right permutable 300 317
Right PF-ring 514—515
Right PP-ring 249 261
Right principally injective ring 119 382 412
Right regular module 2
Right regular ring 199 201
Right reversible 300 317
Right Rickart *-ring 265
Right Rickart ring §7D 270—271 350 377
Right ring of fractions 299
Right self-injective ring §3B 98 262—263 321 359 362 365 377 426 538
Right semihereditary ring 43 188 §7E
Right singular ideal 247 252—253 362
Right T-nilpotent 340
Rim, D.S. 457
Rings admitting dualities 525 526 533—534 540
Rio, A. del 504
Rizvi, ST. 227
Robinson, A. 297
Robson, J.C. 45 74 112 288 344—345 464 468 479
Rosenberg, A. 96 116
Rota, G.-C. x
Rotman, J. x 22 156
Rowen, L.H. 156 158 383
Samuel, P. 84 195
Sandomierski's Theorem 266
Sandomierski, F.L. 242 266 540 541
Schanuel module 29 56
Schanuel's lemma 50 §5A 178
Schanuel, S. 29 165—166 178
Schelter, W. 201
Schmickler-Hirzebruch, U. vii
Schmidt, O.Ju. 85
Schmidt, S.E. x
Schoepf, A. 74—75
Schreier, O. 347
Schroeder — Berstein for injectives 116
Schroeder, E. 116
Self-injective ring §3B 67 226
Semi-artinian module 269
Semilocal Kasch ring 283 285
Semilocal ring xviii 7 38 200 356 363—364 476 495
Seminormal 41
Semiperfect ring 161 363—364 492 523—524
Semiprimary ring xviii 111 §5E 495
Semiprime ideal xviii
Semiprime right Goldie ring 324 330 342 344 346
Semiprime ring xviii 324 §11D 343 §14A
Semireflexive module 144
Semisimple ring xviii 111 224 241 262 324 378
Serre subcategory 520
Serre — Auslander — Buchsbaum Theorems 194 198
Serre's Conjecture 38 177 492
Serre, J.-R. 38 122 177 194 197 520
Shapiro, D.B. x 3 23
Sharifi, R. x
Shepherdson, J.C. 19 233 294
Shock's Theorems 234 244 272
Shock, R.C. 234 244 252 272 329 354
Simon, J.J. 504
Simple (Wedderburn) components xviii 330 343
Simple injectives §3H
Simple module xviii
Simple ring 12
Singular module 247 269 501
Singular submodule §7 327
Skew polynomial ring 295 308 398
Small object 501
Small submodule 74
Small's examples 46 169 204 354—355
Small's Theorems 263 267—268
Small, L.W. x 18 45—47 169 203 204 263 267—268 283 288 305 328 339 344—345 349 354 368
Smith, R.R. 223 227 418
Smith, T.L. x
Socle xviii 242 251
Soublin, J.R. 143
Sridharan, R. 55
Stably finite ring 5 7 18—19 293
Stably free module 203
Stafford, J.T. 201 354
Stallings, J.R. 504
Standard module 100 117
Steinitz Replacement Theorem 209
Steinitz, E. 209
Storrer, H.H. 272
Strong rank condition 10 12 19 135 319
Strongly  -regular ring 321—322
Strongly indecomposable module 84
Strongly regular ring 297—298
Strooker, J.R. 18 203
Subdirectly irreducible rings 158 419 454 539
Subject Index 555
Support 58
Suslin, A.A. 38 177 492
Swan, R.G. x 39 42 59 201
Symmetric algebra §16F 441 456—457
Symmetric ring of quotients 385
Tachikawa, H. 443
Talintyre, T.D. 345 349
Tate, J.T. 365
Third Dual Theorem 519
Thrall, R.M. 407
Tor-functor 186—187
Torsion submodule 163 319
Torsion-free module 44 73 127 146 222 319
Torsionless module 144—146 413 510—511 519—520
Total ring of quotients 59 303
Trace ideal 51
Trace map 17 504
Trivial extension 37 68 282 312 513
Trjitzinsky, W.J. 300
U-torsionless 519
Uniform dimension §6 209 234 316 528
Uniform module §3F 84 235
Unimodular Column Lemma 21
Unique factorization domain (UFD) 56 164 198 203
Unit-regular element 270
Utumi, y. 207 226 240 272 357 359 380
V-ring 97 98
Valette, J. 457
Vamos, R. 119 505 534 537
Varadarajan, K. 213
Vasconcelos, W.V. 18 161
Vazirani, M. x
Villamayor's Theorem 129
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