McConnell J.C., Robson J.C. — Noncommutative Noetherian Rings :: Электронная библиотека попечительского совета мехмата МГУ

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McConnell J.C., Robson J.C. — Noncommutative Noetherian Rings

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Название: Noncommutative Noetherian Rings

Авторы: McConnell J.C., Robson J.C.

Аннотация:

Provides a comprehensive account of the major developments in this important branch of ring theory which have taken place over the past 30 years. Much of the material which comprises this volume has not appeared anywhere in book form before, and the authors have improved and simplified many of the accounts available in journals. The first few chapters form a ``basic course'' which introduces the reader to the subject. Subsequent chapters are each relatively self-contained, so that readers interested in a particular subject can easily consult the sections they want. Specific topics covered include rings arising from matrices, differential operators, and Lie algebras. Contains extensive references.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 636

Добавлена в каталог: 11.06.2008

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Предметный указатель

,       see “Weyl algebra”
      see “Weyl algebra”
      6.6.18 (see also “Weyl algebra”)
, polynomials over      9.6.12
, subfields of      6.6.18
-group      see “Grothendieck group”
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$       1.8.7
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , being Dedekind domain      5.2.11 7.11.3
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , being simple Noetherian      1.8.7
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , global dimension of      7.5.4
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , global dimension of overrings of      9.1.13
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , Krull dimension of      6.5.4 6.6.12
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , Krull dimension of overrings of      9.1.13
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , matrices over      7.11.7
$P_{\lambda}(k)$ , $P_{\lambda_1,...,\lambda_n}(k)$ , skew group ring over      7.8.14 12.7.16
$\mathbb{S}^n$       see “Coordinate ring”
$\mathcal{A}(V,\delta,\Gamma)$       14.8.1 ff
a.c.c      0.1.2
Additive function      12.1.7
Additive reduced rank being      4.1.2
Additivity      4.5.1 ff
Additivity, principle      4.5.9 14.0.0
Adjoint representation      14.1.2
Ado and Iwasawa’s Theorem      1.7.1
Affiliated chain      4.4.6
Affiliated prime      4.3.4
Affiliated sequence      4.4.6
Affine algebra      8.1.9
Affine PI algebra      13.10.1 ff
Algebra, affine      8.1.9
Algebra, almost commutative      8.4.2
Algebraic Lie algebra      14.7.2
Almost centralizing, derivation ring being      15.1.20
Almost centralizing, extension      8.6.6
Almost commutative algebra      8.4.2
Almost commutative algebra, not      14.3.9
Almost normalizing extension      1.6.10
Almost normalizing extension, generic flatness of      9.4.11
Almost normalizing extension, Noetherian      1.6.14
Amitsur — Levitzki theorem      13.3.3
Annihilator      2.1.10
Annihilator, ideal      2.2.15
Annihilator, maximal      2.3.2
Antichain      6.1.1
AR ring      4.2.3
Arithmetic of ideals      5.2.9
Artin radical      4.1.7
Artin — Procesi theorem      13.7.14 13.11.7
Artin — Rees property      4.1.10 4.2.3
Artin — Rees property, and localization      4.2.9 ff 6.8.21
Artin — Tate lemma      13.9.10
Artin — Wedderburn theory      0.1.9
Artinian quotient ring, additivity and      4.5.9
Artinian quotient ring, affiliated primes and      4.4.10
Artinian quotient ring, and largest stable ideal      6.9.10
Artinian quotient ring, existence of      4.1.4
Artinian quotient ring, FBN and      6.8.16
Artinian quotient ring, hereditary ring has      5.4.2
Artinian quotient ring, ideal invariance and      6.8.15
Artinian quotient ring, Krull dimension and      6.8.1 ff
Artinian, module      0.1.2
Artinian, ring      0.1.6
Asano prime ring      5.2.7
Asano prime ring, PI      13.9.15
Associated graded ring (of filtered ring)      1.6.1 ff
Associated graded ring (of filtered ring), of      12.1.10 12.3.5 12.6.1
Associated graded ring (of filtered ring), being generically flat      9.4.9
Associated graded ring (of filtered ring), being integral domain      1.6.6
Associated graded ring (of filtered ring), being Noetherian      1.6.9
Associated graded ring (of filtered ring), being non-Noetherian      8.3.9
Associated graded ring (of filtered ring), being prime      1.6.6
Associated graded ring (of filtered ring), GK dimension of      8.1.14 8.3.20 8.6.1 8.7.6
Associated graded ring (of filtered ring), global dimension of      7.6.18
Associated graded ring (of filtered ring), Krull dimension of      6.5.6
Associated graded ring (of filtered ring), module theory of      7.6.1 ff
Associated graded ring (of filtered ring), of derivation ring      15.4.5 ff
Associated graded ring (of filtered ring), of enveloping algebra      1.7.5
Associated graded ring (of filtered ring), of filtered ring      1.6.4
Associated prime      4.3.9 4.4.2 4.4.4
Augmentation ideal of enveloping algebra      14.3.8
Augmentation ideal of graded ring      12.2.3
Augmentation ideal of symmetric algebra      15.1.18
Augmentation map      14.3.8
Automorphism, inner      1.8.2
Automorphism, outer      7.8.12
Automorphism, X-inner      10.3.10 10.6.15
Azumaya      13.7.6 13.7.13
Azumaya algebra      13.7.6 13.7.13
Azumaya, $\delta$ -symmetric      14.8.3
Azumaya, central separable      13.7.8
Azumaya, central simple      5.3.4
Azumaya, constructible      9.4.12
Azumaya, exterior      13.4.5
Azumaya, filtered      9.4.9
Azumaya, of group      10.3.13 10.4.6
Azumaya, somewhat commutative      8.6.9
Azumaya, symmetric      15.1.18
Basic, composition series      11.6.2
Basic, dimension      11.6.2 11.8.6
Basic, element      11.8.7
Bass’ theorem      11.7.4 11.7.13
Bernstein number      8.4.7
Bimodule, condition      4.5.7
Bimodule, prime      4.3.4
Bimodule, question      6.4.11
Bound      10.1.7
Bounded      6.4.7
Bounded, fully      6.4.7
Bracket product      1.7.1
Brandt groupoid      5.2.14
c-integral      5.3.2
Cancellation of modules      11.4.1 ff 11.7.1 11.8.7
Cancellation, rank      11.5.20
Capelli polynomial      13.5.5
Category, admissible      12.4.2
Category, equivalence      3.5.7 3.7.5
Category, Grothendieck group of      12.4.3
Catenary property      13.10.13
Catenary property in U(g)      14.10.2
Central extension      13.1.11
Central polynomial      13.5.2 13.6.1
Central separable algebra      13.7.8
Central simple algebra      5.3.4 13.3.1
Central simple algebra, having central polynomial      13.6.3
centralizer      3.2.6 10.3.8
Centralizing sequence      4.1.13
Centralizing sequence, in enveloping algebra      14.3.4
Characteristic, closure      13.9.2
Characteristic, ideal      8.7.6
Class group, ideal      12.1.6
Class group, projective      12.1.5
Classical order      5.3.5
Classical order, having central polynomial      13.6.3
CLIQUE      4.3.7
Closed centrally      10.3.13
Closed G      10.3.13
Closed normally      10.3.13
Closure, central      10.3.13
Closure, G      10.3.13
Closure, normal      10.3.13
Codeviation      6.1.8
Common multiple property      2.2.5
Complement      2.2.3
Completely faithful module      5.7.3
Completely faithful module and stable range      6.7.7
Completely integrally closed      5.1.3
Completely integrally closed, characterization of      5.3.3
Completely prime ideal      0.2.2
Completely prime ideal in enveloping algebra      14.2.11
Completely solvable      7.5.7 14.1.8

Compressible      6.9.3
Constructive algebra      9.4.12
Constructive algebra, derivation ring being      15.1.22
Context, equivalent      3.6.4
Context, Morita      1.1.6
Context, prime      3.6.5
Coordinate ring of $\mathbb{S}^1$ , of      12.1.6
Coordinate ring of $\mathbb{S}^1$ , of derivation ring of      15.4.8
Coordinate ring of $\mathbb{S}^1$ , derivations of      15.3.13
Coordinate ring of $\mathbb{S}^1$ , is Dedekind domain      7.8.14
Coordinate ring of $\mathbb{S}^1$ , overling of      12.7.8
Coordinate ring of $\mathbb{S}^2$ , Der - is not free      15.3.15
Coordinate ring of $\mathbb{S}^2$ , has stably free module      11.2.3
Coordinate ring of $\mathbb{S}^2$ , ranks of      11.5.4
Coordinate ring of algebraic variety      15.0.0
Coordinate ring of cusp      15.3.12 15.4.10
Critical      6.2.9
Critical, composition series      6.2.19
Critical, for dimension function      6.8.25
Critical, ideal      6.3.4
Crossed product $R\ast G$       see “Group ring”
Crossed product, $R\ast g$       1.9.9
Crossed product, $R\ast U(g)$       see “Enveloping algebra”
Cusp      see “Coordinate ring”
Cutting down      10.2.4
Cutting down in enveloping algebra      14.2.5 14.5.4
Cutting down in fixed ring      10.5.15
Cutting down in group ring      10.5.6
d.c.c      0.1.2
Dedekind domain/prime ring      5.2.10
Dedekind domain/prime ring, $1\frac12$ generators in      5.7.12
Dedekind domain/prime ring, commutative      5.2.8 5.7.18
Dedekind domain/prime ring, module theory of      5.7.1 ff 7.11.4 11.7.14 11.8.7
Dedekind domain/prime ring, PI      13.9.14
Dedekind domain/prime ring, simple      7.11.1 ff
Degree of function      8.1.7
Degree of ordinal      6.1.9
Degree of polynomial      1.2.8 9.6.6
Degree of polynomial element      6.9.17
Degree of polynomial identity      13.1.2
Degree, in filtered module      7.6.7
Degree, minimal      13.2.2
Degree, PI      13.3.6 13.6.7
Degree, total      9.4.15
Degree, transcendence      8.2.14 13.10.5
Denominator set      2.1.13
Dense, right ideal      10.3.4
Dense, subring      0.3.5
Density theorem      0.3.6
Derivation ring      15.1.4 ff
Derivation ring, associated graded ring of      15.4.5 ff
Derivation(s) and localization      14.2.2
Derivation(s) and prime ideals      14.2.3
Derivation(s), $\sigma-$       1.2.1
Derivation(s), inner      1.8.2
Derivation(s), k-      1.7.10 15.1.2
Derivation(s), k-, to module      15.1.7
Derivation(s), locally nilpotent      14.6.4
Derivation(s), universal      15.1.8
Derivation(s), universal bimodule of      8.7.3
Deviation      6.1.2
Differential operator(s)      see also “Derivation ring”
Differential operator(s), asymmetry of      15.6.5
Differential operator(s), order of      15.4.11 15.5.2
Differential operator(s), ring of      15.0.0 ff 15.5.1 15.6.5
Differentials (Kahler)      15.1.8 15.6.1
Differentials (Kahler) of regular ring      15.2.12
Dimension, basic      11.6.2 11.8.6
Dimension, classical Krull      6.4.4
Dimension, exact function      6.8.4
Dimension, flat      7.1.4
Dimension, function      6.8.4
Dimension, Gabriel      6.10.0
Dimension, Gelfand — Kirillov      8.1.11 8.1.16
Dimension, GK      8.1.11 8.1.16
Dimension, global      7.1.8
Dimension, Goldie      2.2.10
Dimension, injective      7.1.3
Dimension, Kronecker      11.5.9
Dimension, Krull      6.2.2
Dimension, projective      7.1.2
Dimension, uniform      2.2.10
Dimension, weak      7.1.4
Dimension, weak global      7.1.9
Discriminant      13.8.11
Dual basis lemma      3.5.2
Dual module      3.4.4
Eigen, ring      1.1.11
Eigen, value      14.1.16
Eigen, vector      14.1.15
Eisenbud — Evans theorem      11.7.4
Element, automorphic      10.1.3
Element, c-integral      5.3.2
Element, centralizes      10.1.3
Element, homogeneous      1.6.3 7.6.3 10.6.7
Element, integral      5.3.2
Element, minimal      9.4.18
Element, nilpotent      0.2.5
Element, normal      4.1.10
Element, normalizes      10.1.3
Element, regular      2.1.2
Element, strongly nilpotent      0.2.5
Elementary group      11.3.5
Elementary range      11.3.9
Elementary rank      11.3.10
Endomorphism property over k      9.1.4
Endomorphism property, over K      9.2.3
Endomorphism ring, algebraic      9.1.4 ff
Endomorphism ring, and matrices      8.2.8
Endomorphism ring, finite dimensional      9.5.1 ff
Endomorphism ring, of uniform ideal      3.3.5
Endomorphism ring, over PI ring      13.4.9
Endomorphism ring, over semiprime ring      3.4.1 ff
Enveloping algebra (skew, crossed product)      1.7.1 ff 14.0.0
Enveloping algebra (skew, crossed product), of      12.6.14
Enveloping algebra (skew, crossed product), associated graded ring of      1.7.5
Enveloping algebra (skew, crossed product), being .almost commutative      8.4.1 ff
Enveloping algebra (skew, crossed product), being almost centralizing      8.6.6
Enveloping algebra (skew, crossed product), being almost normalizing      1.7.14
Enveloping algebra (skew, crossed product), being constructible      9.4.12
Enveloping algebra (skew, crossed product), being integral domain      1.7.5 1.7.14
Enveloping algebra (skew, crossed product), being maximal order      5.1.6
Enveloping algebra (skew, crossed product), being Noetherian      1.7.4 1.7.14
Enveloping algebra (skew, crossed product), being prime      1.7.14
Enveloping algebra (skew, crossed product), being regular      7.7.5
Enveloping algebra (skew, crossed product), being somewhat commutative      8.6.10
Enveloping algebra (skew, crossed product), crossed product      1.7.12
Enveloping algebra (skew, crossed product), crossed product construction      1.9.7 1.9.9
Enveloping algebra (skew, crossed product), example of      15.3.14
Enveloping algebra (skew, crossed product), GK dimension of      8.1.15 8.2.10
Enveloping algebra (skew, crossed product), global dimension of      7.5.7 7.6.10
Enveloping algebra (skew, crossed product), having finite endomorphism ring      9.5.5
Enveloping algebra (skew, crossed product), having projectives stably free      12.3.3
Enveloping algebra (skew, crossed product), Krull dimension of      6.5.7 6.6.2
Enveloping algebra (skew, crossed product), not simple      1.7.5
Enveloping algebra (skew, crossed product), Nullstellensatz for overrings of      9.4.22
Enveloping algebra (skew, crossed product), Nullstellensatz in      9.1.8 14.4.1
Enveloping algebra (skew, crossed product), of sl(2, k)      8.5.12
Enveloping algebra (skew, crossed product), of solvable Lie algebra      14.1.1 ff
Enveloping algebra (skew, crossed product), Poincare — Birkhoff — Witt theorem for      1.7.5 1.9.7 1.9.9
Enveloping algebra (skew, crossed product), prime ideals in      14.2.1 ff 14.3.1
Enveloping algebra (skew, crossed product), primitive ideals in      14.4.1 ff
Enveloping algebra (skew, crossed product), second layer condition in      4.3.14
Enveloping algebra (skew, crossed product), semicentre of      14.4.6
Enveloping algebra (skew, crossed product), simple      1.8.3
Enveloping algebra (skew, crossed product), skew      1.7.10
Enveloping algebra (skew, crossed product), smash product      1.9.7
Enveloping algebra (skew, crossed product), stably free ideals of      11.2.14
Enveloping algebra (skew, crossed product), standard monomials in      1.7.5
Enveloping algebra (skew, crossed product), universal property of      1.7.2

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