Drensky V., Formanek E. — Polynomial Identity Rings :: Электронная библиотека попечительского совета мехмата МГУ

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Drensky V., Formanek E. — Polynomial Identity Rings

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Название: Polynomial Identity Rings

Авторы: Drensky V., Formanek E.

Аннотация:

A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx).

Язык:

Рубрика: Математика/Алгебра/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Добавлена в каталог: 09.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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 ${GL}_{d}$ -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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