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Karpilovsky G. — The Jacobson radical of classical rings
Karpilovsky G. — The Jacobson radical of classical rings

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Название: The Jacobson radical of classical rings

Автор: Karpilovsky G.

Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 584

Добавлена в каталог: 23.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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, $\lambda$-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 $dim_{F}J(Z(FG))$      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 $End_{R}(V)$ to be exchange ring      50
Criterion for $End_{R}(V)$ to be idempotent-lifting      48
Criterion for $J(F^{\alpha}G)$ 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 $F^{\alpha}G$      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, $\pi$-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 $\pi$-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
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