Abelian group 182
Abelian group, n-divisible 182
Abelian group, n-torsion 182
Abelian group, uniquely divisible by n 182
Adjan 357
Algebra 1
Algebra of finite representation type 487
Algebra, algebraic 106
Algebra, cancellative 250
Algebra, definable over a subfield 123
Algebra, finitely generated 106
Algebra, free 172
Algebra, free commutative 171
Algebra, Frobenius 126
Algebra, graded 160
Algebra, homomorphism of 2
Algebra, nilpotent-free 313
Algebra, P.I. 107
Algebra, separable 118
Algebra, strongly M-graded 161
Algebra, symmetric 126
Algebraic element 102 106
Algebraically independent set 105
Amitsur 106 113 115 271 272
Amitsur's Theorems 106 113 115 271
Annihilator 18 193
Ascending chain condition 51
Ascending series 375
Augmentation 172 336
Augmentation ideal 172 336
Automorphism 259
Automorphism of locally finite order 259
Automorphism,  -nilpotent 259
Automorphism, bounded 373
Azumaya 88 149 155
Balanced map 89
Basis for J(Z(FG)) 479
Basis for Z(FG) 494
Baumslag 229
Bedi 258 262 269 279
Bedi — Ram theorem 279
Beidar 107
Beidar's theorem 107
Bergman 160 235
Bilinear form 125
Bilinear form, associative 125
Bilinear form, nonsingular 125
Bilinear form, symmetric 125
Bimodule 30
Blackburn 473 478
Block 139
Block idempotent 139
Blocks of p-nilpotent groups 478
Bourbaki 105 111 116 117 118 187 188
Bovdi 172 286 287 359
Bovdi's theorems 286 359
Brauer 145 464 467 474 501 505
Brauer homomorphism 475
Brauer's Theorems 145 467 505
Brockhaus 472 502 503
Brockhaus theorem 472
Burnside 491
Cancellation property 47
Canonical homomorphism 12 95
Canonical injection 184
Central character 139
Central normalizing basis 276
Central series 230
Characterization of  521
Clifford's theorem 213
Coboundary 180
Cocycle 180
Cohen 223
Cohn 41
Cohomologous cocycles 181
Cohomology class 181
Comaximal ideals 12
Commutator submodule 358
Commutator subspace 144
Commuting subalgebras 94
Compatible action 303
Complement 493
Completeness 43
Composition series 7
Composition series, equivalent 7
Composition series, length of 7
Conjugate elements 102
Conjugate of module 212
Connell 291 349 350 351 363
Control 453
Controller 453
Core 240
Crawley 46
Criterion for  to be exchange ring 50
Criterion for to be idempotent-lifting 48
Criterion for  to be nilpotent 310 312 333
Criterion for algebra to be Frobenius 128 129
Criterion for algebra to be separable 118
Criterion for algebra to be strongly graded 162 210
Criterion for algebra to be symmetric 128 129
Criterion for algebra to be uniserial 154 155
Criterion for artinian algebra to be separable 122
Criterion for augmentation ideal to be locally nilpotent 351
Criterion for augmentation ideal to be nil 351
Criterion for augmentation ideal to be nilpotent 350
Criterion for block to be principal 477
Criterion for containment in J(R) 20
Criterion for each block to be quasi-primary 486
Criterion for element to be invertible 23
Criterion for endomorphism to be local 47
Criterion for equality of the Jacobson and nilpotent radicals 310
Criterion for existence of blocks 11
Criterion for existence of composition series 7
Criterion for existence of projective cover 132
Criterion for extension to be Galois 104
Criterion for extension to be normal 102
Criterion for extension to be purely inseparable 104
Criterion for FG to satisfy polynomial identity 366
Criterion for field to be perfect 104
Criterion for field to be splitting 138
Criterion for finite decomposition 5
Criterion for group algebra to be indecomposable 479
Criterion for group ring to be semisimple 291
Criterion for I(G) to be locally nilpotent 351
Criterion for I(G) to be nilpotent 350
Criterion for ideal to be graded 163
Criterion for ideal to be maximal 33
Criterion for ideal to be nilpotent 52 53
Criterion for ideal to be primitive 33
Criterion for ideal to be quasi-regular 20
Criterion for ideal to be superfluous 20
Criterion for induced module to be semisimple 197
Criterion for J(A) to be nil 106
Criterion for J(FG) to be locally nilpotent 340
Criterion for J(FG) to be nilpotent 357
Criterion for J(FG) to be of maximal dimension 502
Criterion for J(FG) to be of minimal dimension 503
Criterion for J(R) to be nilpotent 54 55
Criterion for J(RG) to be locally nilpotent 340
Criterion for J(RG) to be nil 350
Criterion for lifting idempotents 42
Criterion for local nilpotence of nil ideals 367
Criterion for module to be absolutely simple 137
Criterion for module to be artinian 4 5
Criterion for module to be flat 187
Criterion for module to be graded-semisimple 204
Criterion for module to be indecomposable 45
Criterion for module to be noetherian 4 5
Criterion for module to be projective 75
Criterion for module to be semisimple 9
| Criterion for module to be simple 18
Criterion for module to have exchange property 48
Criterion for principal block to be quasi-primary 486
Criterion for rad(R) to be nilpotent 28
Criterion for ring to be artinian 35
Criterion for ring to be idempotent-lifting 38 39
Criterion for ring to be indecomposable 11
Criterion for ring to be local 45
Criterion for ring to be prime 25 33
Criterion for ring to be primitive 33
Criterion for ring to be reduced 348
Criterion for ring to be regular 34
Criterion for ring to be regular noetherian 35
Criterion for ring to be semiperfect 44
Criterion for ring to be semiprime 27
Criterion for ring to be semiprimitive 20
Criterion for ring to be semiprimitive artinian 35
Criterion for ring to be semisimple 35
Criterion for ring to be simple 33
Criterion for semiprimitivity of  295 297 298 310 314
Criterion for semiprimitivity of crossed products 284
Criterion for semiprimitivity of graded algebras 237 239
Criterion for semiprimitivity of tensor products 121
Criterion for semisimplicity of crossed products 291
Criterion for semisimplicity of graded modules 222 224
Criterion for semisimplicity of tensor products 122
Criterion for separability of algebras 118
Criterion for separability of field extensions 117
Criterion for subalgebras to be linearly disjoint 97
Criterion for subgroup to be finitely generated 300
Criterion for submodule to be fully invariant 64
Criterion for subring to be T-nilpotent 57
Criterion for twisted group algebra to be commutative 297
Crossed product 174
Crossed system 173
Curtis 497 511
Dade 165 210
Dade's theorems 165 210
Defect 476
Defect group 476
Defect group of principal block 477
Degree of unit 202
Dense subring 32
Derived series 229
Descending chain condition 23 51
Diagonal action 303
Direct product of rings 2
Direct sum of modules 2
Domain 289
Eilenberg 130
Essential ideal 51
Essential submodule 73 151
Essentially nilpotent ideal 62
Exchange property 46
Exponent of inseparability 103
Field 101
Field extension 101
Field extension, algebraic 102
Field extension, degree 101
Field extension, finite 101
Field extension, finitely generated 101
Field extension, Galois 104
Field extension, infinite 101
Field extension, normal 102
Field extension, purely inseparable 103
Field extension, purely transcendental 105
Field extension, separable 104
Field extension, separable algebraic 103
Field extension, separably generated 105
Field extension, simple 101
Field extension, transcendental 105
Field, algebraic closure of 102
Field, algebraically closed 102
Field, fixed 104
Field, perfect 104
Field, splitting 102
Finite exchange property 46
Finite left dimension 57
Finite normalizing bimodule 83
Fischer 56 59 60 61 63 81
Fischer — Goldie — Small theorem 60
Fischer's theorems 56 59 63 81
Fitting 71
Fitting's lemma 66
Fitting's theorem 71
Fixed-point space 495
Fong 473
Fong's dimension formula 473
Formal power series 109
Formanek 85 473
Free factor 246
Free product 244
Frobenius reciprocity 185
Fully invariant submodule 64
G-invariant ideal 165
G-prime ideal 254
G-prime radical 254
Galois group 104
Gauss lemma 328
Generalized polynomial 366
Generalized polynomial identity 366
Gorenstein 491 492
Graded group ring 215
Graded homomorphism 162 199
Graded ideal 162 199
Graded isomorphism 162 199
Graded Jacobson radical 207
Graded Maschke's theorem 221
Graded radical 205
Graded submodule 199
Graded unit 202
Graded-primitive ideal 207
Graded-superfluous submodule 206
Group 169
Group algebra 170
Group of bounded automorphisms 373
Group of finite exponent 231
Group of p-length 1 491
Group ring 170
Group,  -group 233 390
Group, abelian 182
Group, divisible 345
Group, exponent 231
Group, free 229
Group, free solvable 229
Group, Frobenius 492
Group, hyper 428
Group, L-linear 404
Group, linear 404
Group, locally C-group 228
Group, locally finite 169
Group, locally free 229
Group, locally normal 351
Group, locally p-solvable 403
Group, locally solvable 229
Group, n-divisible 182
Group, nilpotent 230
Group, noetherian 230
Group, p-constrained 478
Group, p-nilpotent 478
Group, p-solvable 319
Group, polycyclic-by-finite 240
Group, residually -group 233
Group, residually C-group 228
Group, subdirect product of 228
Group, torsion 231
Group, uniquely divisible by n 182
Group-theoretic class 228
Gruenberg 231
Gruenberg's theorem 231
|
|
|
О проекте