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| Drensky V., Formanek E. — Polynomial Identity Rings |
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| Предметный указатель |
Affine 173
Affine algebra 177
Algebra of invariants 59
Alternating 141
Amitsur — Levitzki theorem 37 133 143 145
Amitsur, S.A. 140 143 151 155 158 159 161 169 178 180 181
Antichain 103
Artin — Tate lemma 177 178
Artin's theorem 133 165 169 170 174
Artin, M. 169 170
Associated trace function 63
Azumaya algebra 133 163—165 170 173 174
Basis of identities of algebra 8
Basis of T-ideal 8
Beneish, E. 191
Bergman gap theorem 99
Bessenrodt, C. 191
Bimodule 152
Birkhoff theorem 115
Bounded degree 141
Branching theorem 28
Brauer group 190
Braun's characterization of Azumaya algebras 165
Braun, A. 133 165 173
Capelli identity 6
Capelli polynomial 141 169
Cauchon, G. 175
Cayley — Hamilton theorem 143
Central 5eparable 165
Central polynomial 49 133 143 147 148 160 165 169 170 173 174
Central simple algebra 153 160 170 173
Chain 103
Chevalley — Jacobson density theorem 151 152
Cocharacter 32
Codimension 19
Codimension sequence 19
Codimension series 24
Commutator 6
Comparable elements 103
complexity 90
Complexity function 24
Consequence of identities 8
Constant rank 164 170
Decomposable word 87
Dehn, M. 151
Dense ring of linear transformations 152 153
Density theorem 151 152
Derivation 84
Diagram see “Young diagram”
Dicks, W. 166
Dilworth theorem 103
Double Capelli identity 40
Double staircase 40
Drensky, V.S. 143
Elementary symmetric function 144
Enveloping algebra 164
Equivalent polynomial identities 8
Eulerian graph 37
Evaluation map 164
Exponential codimension series 24
Exponential generating function 23
Exterior algebra 7 140 143 147
Extremal variety see “Minimal variety”
Finite basis property 10
Finitely presented algebra 60
First fundamental theorem of invariant theorv 60
Formanek polynomial 148 154 160 174
Formanek, E. 133 147 148 160 174 175 185 189 191
Free associative algebra 5
Free nonunitary algebra 5
Free semigroup 87
Frobenius, F.G. 143
Fully invariant ideal 8
Fully invariant subgroup 138
Fundamental trace identity 63
Gelfand — Kirillov dimension 98
Generating function 23
Generic division ring 134 183 185 189
Generic flatness 175
Generic matrix 13 147
Generic matrix algebra 13
Generic matrix ring 134 148 179
Goldie's Theorem 133 159 173
Goldie, A.W. 169
Good permutation 105
Graded vector space 20
Grassmann algebra 7 140 143
Grassmann hull 111
Growth function of algebra 97
Growth of algebra 98
Hall identity 7
Hall, M. 151
Height 88
Height, essential height 95
Highest weight vector 31
Hilbert algebra 177 178
Hilbert series 21
Hilbert's Nullstellensatz 177
Homogeneous 137
Homogeneous component 138
Homogeneous polynomial identity 10
Homogeneous system of parameters 67
Hook formula 28
Identity of algebraicity 41
Induced module 28
Jacobson radical 155 157
Jacobson ring 177 178
Kaplansky's Theorem 133 140 151—154 159 160 169 170 178
Kaplansky, L 151 153 155
Katsylo, P.I. 191
Kemer, A.R. 133 173
Kirillov, A.A. 187
| Kostant, B. 143
Krull, W. 173
Kurosh problem 89
Kurosh problem, for PI-algebras 89
LeBruyn, L. 191
Levitzki, J. 143 155 156 159
Linearization 11
Long commutator 6
MacDonald, I.G. 144
Matrix concominants 67
Matrix invariants 62
Maximal subfield 153
Merkurjev — Suslin theorem 190
Minimal variety of given exponent 114
Mixed Cayley — Hamilton identity 64
Mixed formal Cayley — Hamilton polynomial 64
Mixed free trace algebra 64
Mixed trace algebra 61
Molien formula 60
Multigraded vector space 20
Multihomogeneous identity 10
Multilinear 137
Multilinear polynomial identity 10
Nagata — Higman theorem 75
Newton, I. 144
NIL 156 161
Noetherian 173 175
Noetherian ring 175
Nonmarrix identity 91
NullsteHensatz 177 178
Opposite ring 164
Orthogonal invariants 69
Orthogonal invariants, absolute 69
Orthogonal invariants, even 69
Orthogonal invariants, odd 69
Pappus theorem 151
Partially ordered set 103
Partition 26
PI-algebra 6 139
PI-degree 90 154
Pi-equivalent algebras 115
Pi-ring 139
Poincare series see “Hilbejt series”
Polynomial  -module 29
Polynomial identity 6 138
Polynomial representation of GLd 29
Posner's theorem 133 134 155 159 160 169 174 180 181 183 186
Posner, E.C. 155 159 160
Power symmetric function 144
Prime 155
Prime radical 161
primitive 151
Procesi, C 143 150 169 178 180 183—187 191
Projective module 163 164 167
Proper polynomial identity 139
Pure Cayley — Hamilton identity 64
Pure formal Cayley — Hamilton polynomial 64
Pure trace algebra 61
Pure transcendental extension 134 183
Rank of projective module 164
Rational function field 183 187 189
Razmyslov transform 51
Razmyslov — Kemer — Braun theorem 96
Razmyslov, Y.R. 133 143 147 173
Regev codimension theorem 107
Regev tensor product theorem 107
Regev, A. 162
Relatively free algebra 9 179
Representable algebra 96
Ring of formal power series 157
Ring without unit (rng) 155
Rosset, S. 143 145
Rowen, L.H. 159 160 169
Schelter, W. 133 169 173
Schofield, A. 191
Schur function 31
Schur's lemma 152
Second fundamental theorem of invariant theory 60
Semiprime 157
Semiprimitive 157
Separable algebra 165
Shirshov height theorem 88
Simple ring 153
Simultaneous conjugation 62
Small, L.W. 174
Specht problem 9
Specht property 10
Spechtian algebra 10
Stablv birational 190
Stably rational 190
Staircase arguments 38
Standard identity 6
Standard polynomial 141
Standard tableau 27
Subdirect product 157
Svlvester, J.J. 183
Symmetric function 144
T-ideal 8 138
T-prime ideal 110
T-semiprime ideal 110
Tableau see “Young tableau”
Trace identities 143
Trace polynomial identity 39
Unirational 187
Variety of algebras 9
Wagner, W. 151
Weak polynomial identity 50
Weak polynomial identity, essential weak identity 50
Wedderburn's Theorem 154
Weyl algebra 140
Young diagram 26
Young tableau 27
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