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| Lam T.Y. — A first course in noncommutative ring theory |
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| Предметный указатель |
Roiter, A.V. 123
Row rank (of a matrix) 227
Rowen, L.H. 30 370 381 382
Samuel, P. 2 195 196 305 383
Sanov, I.N. 150
Scalar extension 78 ll0
Scharlau — Tschimmel Theorem 289
Scharlau, W. 289
Schmidt, E. 282
Schmidt, O.Ju. 293 301 302
Schofield's examples 248
Schofield, A. 248
Schreier, O. 255 275 277
Schur's lemma 35
Schur's Theorems 138 154
Schur, I. 35 82 108 154
Scott's Theorem 225
Scott, W.R. 225
Seidenberg, A. 306
Semigroup ring 8 198
Semilocal ring 311
Semiperfect commutative ring 350
Semiperfect endomorphism ring 348
Semiperfect ring 346
Semiprimary ring 55 317
Semiprime group ring 170
Semiprime ideal 167
Semiprime matrix ring 172
Semiprime polynomial ring 171
Semiprime ring 163 168
Semiprimitive ring see Jacobson semisimpie ring
Semiprimitivity Problem for group rings ix
Semisimpie Lie algebra 51
Semisimpie module 26 27 31
Semisimpie operator 42
Semisimpie ring 26 28 29 32
Semisimplicity 1 26
Separable algebra 113
Separable algebraic extension, 79—80 180
Separable element 257
Separable maximal subfield 257
Serre, J.-P. 275 277
Sfield (or division ring) 213
Shapiro, D.B. ix
Sign character 139
Simple (or Wedderburn) component 37
Simple artinian ring 38 39 40 253
Simple decomposition 37
Simple domain 48
Simple Lie algebra 51
Simple module 26 28
Simple ring 3 32 33 43—48
Skew field (or division ring) 213
Skew group ring 14 15 247 250
Skew Laurent polynomial ring, 11 46
Skew Laurent series ring 10 243
Skew polynomial ring 10 62 178—179 187 230 233
Skew power series ring 10 297
Skew symmetric matrix 50
Small (or superfluous) submodule, 358
Small, L.W. 381 382
Smith, T.L. ix
Snapper's Theorem 70
Snapper, E. 70
Socle (left or right) of a ring, 69 186 202—203 205
Socle of a module 69
Solitar, D. 103
Solvable ideal 51
Solvable Lie algebra 156
Splitting field (of a group) 126
Splitting field (of a polynomial) 113
Splitting field (of an algebra) 112
Square-product 285
Stably free module 316
Steinitz Isomorphism Theorem, 302
Steinitz, E. 302
Stonchewer, S.E. 146
Strictly maximal subfield 236
Strongly (or completely) prime ideal, 206
Strongly indecomposable module, 298
Strongly nilpotent element 180
Strongly yon Neumann regular ring, 211
Subdirect product 203
| Subdirectly irreducible ring 204
Subdirectly reducible ring 204
Subnormal subgroup 156
Subring 3
Superfluous (or small) submodule, 358
Support 242
Suprunenko, D.A. 157
Swan's example 305—306
Swan, R.G. 145 305 314
Sylow, L. 158
Symmetric algebra 13
Szele, T. 275 286
Takahashi, S. 145
Tensor algebra 12
Tensor product of algebras 221 251
Tetrahedral group 6 140
Thrall, R.M. 123
Tignol, J.-p. ix 233 236
Topologically nil element 90
Torsion group 150 154
Torsion-free group 82 95 97 100
Totally positive element 280 286
Trace 86 91 92 117
Trace Lemma 151
Transfer homomorphism 96
Trazom, A.W. 398
Triangular ring 17 18
Trivial idempotent 293
Trivial unit (in group rings) 94 95 101 142
Tschimmel, A. 289
Twisted (or skew) polynomial, 7 10
Two-sided ideal 3
Unipotent group 157
Unipotent operator 156
Unipotent radical 156 160
Uniserial module 61
Unit (or invertible element) 4 24
Unit of group rings 8
Unit Problem for group rings, 95
Unitriangular group 157
Unitriangular matrix 157
Universal algebra vii
Universal enveloping algebra 13
Universal property 3 6
Upper central series 223
Upper nilradical 77 163 173—174
Utumi's argument 175
Utumi, y. 175
Valuation ring 296
Vandermonde matrix 273
Vandermonde, A.T. 273
Vandiver, H.S. 215
Varieties of rings vii
Villamayor, O.E. 146
von Neumann regular ring 65—67 69 105 181 334
von Neumann-finite ring 4
Wadsworth's example 291
Wadsworth, A.R. 291
Waerden, van der, B.L. 179
Wallace's Theorem 105
Wallace, D.A.R. 94 105 131
Weak preordering 279
Weakly n-finite ring 317
Wedderburn radical 1 31 51—52
Wedderburn — Artin theorem 1 35
Wedderburn — Artin Theory Chapter 1
Wedderburn's Little Theorem, 104 209 214
Wedderburn's Norm Condition, 233 238
Wedderburn's Theorems 41 104 214 233 265
Wedderburn, J.H.M. vii 1 26 31 35 41 51 104 209 213 214 233 265 302
Well-ordered (WO) set 241
Weyl algebra 7 8 12 14 45 50 202 283
Weyl, H. 7 32
Whaples, G. 201 268
Wigner, E.P. 7
Willenm, W. 146
Witt, E. 13 103 215
Yang, C.T. 256 382
Zariski's Lemma 72
Zariski, O. 2 72 305 383
Zero-divisor 3
Zero-Divisor Problem for group rings ix 95
Zorn, M. 27
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