Beidar K.I., Martindale III W.S., Mikhalev A.V. — Rings with Generalized Identities :: Электронная библиотека попечительского совета мехмата МГУ

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Beidar K.I., Martindale III W.S., Mikhalev A.V. — Rings with Generalized Identities

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Название: Rings with Generalized Identities

Авторы: Beidar K.I., Martindale III W.S., Mikhalev A.V.

Аннотация:

This outstanding reference discusses the latest results concerning the area of non-commutative ring theory known as the theory of generalized identities (GIs) - detailing Kharchenko's results on GIs in prime rings, Chuang's extension to anti-automorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Providing novel proofs of existing results, Rings with Generalized Identities puts the theory of generalized identities on a rigorous basis with the use of skew group rings...presents Beidar's determination of the generators of the T-ideal of generalized polynomial identities in (semi)prime rings...furnishes a thorough proof of the generalized Poincare-Birkhoff-Witt theorem for (restricted) differential Lie algebras, making extensive use of the Diamond Lemma...gives a general account of the extended centroid and rings of quotients...covers a recent solution to a long-standing conjecture of Herstein on Lie isomorphisms...and more.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 531

Добавлена в каталог: 18.11.2009

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Предметный указатель

$\bar T$ -identity      299
$\hat T'$ -identity      418
$\hat T'$ -substitution      418
$\mathcal{T}$ -ideal      259
$\mu$ -derivation      3
$\Omega$ - $\Delta$ -ring      37
$\Omega$ -ring      35
$\rho$ -degree      419
$\rho$ -height      419
$\sigma$ -antiautomorphism      4
$\sigma$ -automorphism      4
$\tau$ -monomial      419
(x,g)-variable      348
*-ideal      156
Action of a group      4
Algebra centrally closed      69
Algebra differential Lie      187
Algebra enveloping      175
Algebra free      11
Algebra Lie      175
Algebra p-Lie      182
Algebra reduced universal enveloping      390
Algebra restricted Lie      182
Algebra tensor      9
Algebra universal enveloping      175
Ambiguity inclusion      16
Ambiguity overlap      16
Ambiguity resolvable      16
Antiautomorphism      3
Arity of operation      34
Automorphism      3
Automorphism Frobenius      332
Automorphism left dependent      93
Automorphism left independent      93
Automorphism S-algebraic      371
Automorphism X-inner      91
Biderivation      456
Central closure      68
Complexity of formula      38
Cover of a Lie algebra      175
Cover of a restricted Lie algebra      182
Degree Frobenius      347
Derivation      2
Derivation inner      2
Derivation of K-algebra      3
Derivation S-algebraic      365
Derivation strongly independent      394
Derivation X-inner      88
DIMENSION      77
Dual sets of vectors      140
Dual spaces      139
Element -reduced      420
Element $\tau$ -homogeneous      215 329
Element (i,j)-pure      32
Element 0-pure      32
Element algebraic      73
Element F-reduced      337
Element Frobenius      345 401
Element irreducible      15
Element k-homogeneous      214 328
Element multilinear      215
Element normalizing      91
Element of finite D-rank      130
Element reduced      307 420
Element skew      156
Element symmetric      156
Element T-multilinear      329
Extended centroid      68 452
F-degree      334
Filter      45
Filter principal      45
Finite C-rank n      233
Form $\mathcal{A}$ -standard      275
Form alternate      158
Form Hermitian      158
Formula(s)      38
Formula(s) atomic      38
Formula(s) equivalent      41
Formula(s) false      41
Formula(s) hereditary      120
Formula(s) Horn      43
Formula(s) multiplicatively stable      43
Formula(s) strictly hereditary      120
Formula(s) strictly multiplicatively stable      43
Formula(s) true      41
g-height      224
g-homogeneous component      252
g-identity      223
g-substitution      223
H-endomorphism      258
Height of element      32
Homomorphism of $\Omega$ -rings      35
Ideal dense      64
Ideal dense right      51
Ideal essential right      53
Ideal minimal left      141
Ideal of an $\Omega$ -ring      35
Ideal right singular      60
Idempotent abelian      234
Idempotent faithful      234

Idempotent minimal      143
Identity -reduced      420
Identity $\tau$ -homogeneous      215 329
Identity F-trivial      334
Identity g-multilinear      225
Identity generalized polynomial      212 227
Identity Jacobi      175
Identity k-homogeneous      214 328
Identity multilinear      215
Identity strict      229
Identity T-multilinear      329
Identity, strict $\hat T'$ -identity      418
Involution      3 156
Involution of the first kind      165
Involution symplectic      164
Involution transpose      164
K-ring      1
Logical symbols      38
Map $\mu$ -semilinear      3
Map $\sigma$ -semilinear      3
Map adjoint map      139
Map balanced      7
Map differential Lie      196
Map n-linear symmetric      455
Map permissable      452
Matrix of bilinear form      164
Module closed      6
Module conjugation      92
Module nonsingular      98
Monomial correct      394
Monomial generalized pivotal      151
Monomial pivotal      151
n-ary predicate      34
Normal form of element      15
O-subgroup      403
Operation      72
Operation 0-ary      34
Operation n-ary      34
Ordering compatible      16
Ordering semigroup      16
Orthogonal completion      106
p-operation      182
Pierce stalk      112
Polynomial -reduced      420
Polynomial additive      338
Polynomial reduced      259
Polynomial standard      21
Product Cartesian      37
Product Jordan      156
Product Lie      156
Product n-fold tensor      8
Product tensor      7
Reduction system      15
Reductions      15
Representation      419
Ring associated division      129
Ring centrally closed      69
Ring commuting      129
Ring Lie      2
Ring multiplication      451
Ring of quotients maximal right      56
Ring of quotients symmetric      66
Ring of quotients two-sided classical      220
Ring of quotients two-sided right      64
Ring orthogonally complete      110
Ring prime      1
Ring primitive      1 129
Ring self-injective      2
Ring semiprime      1
Ring skew group      4
Ring von Neumann regular      61
S-context      6
Sentence      39
Set of transformation units      163
Setting *-maximal      361 422
Setting extended      304
Setting maximal      361 418
Setting of R      302
Socle      142
Standard basis      275
Subset dense      99
Subset orthogonal      99
Subset orthogonally complete      100
Subset total subset      6
Subset weakly dense      6
Substitution      37 212
Support      419
T*-identity      361
T*-substitution      361
T-identity      303 304
T-substitution      302 304
Term      36
Term, leading g-term      317
Trace commuting      456
Trace of n-linear mapping      456
Type symplectic      157
Type transpose      157
Ultrafilter      45
Ultraproduct      47
Variable free      38

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