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


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ring(s), context equivalent      3.6.4
Ring(s), Dedekind      5.2.10
Ring(s), derivation      15.1.4
Ring(s), extension      1.6.2
Ring(s), FBN      6.4.7
Ring(s), filtered      1.6.1
Ring(s), fixed      7.8.1
Ring(s), fully bounded      6.4.7
Ring(s), G-----      13.9.12 14.5.6
Ring(s), generic matrix      13.1.19
Ring(s), Goldie      2.3.1
Ring(s), graded      1.6.3
Ring(s), graded-division      10.3.19
Ring(s), graded-simple      10.3.19
Ring(s), group-graded      10.3.18
Ring(s), hereditary      5.2.2
Ring(s), ideal invariant      6.8.13
Ring(s), irreducible      6.8.17
Ring(s), Jacobson      9.1.2
Ring(s), localization of      2.1.4
Ring(s), locally nilpotent      13.8.5
Ring(s), Morita equivalent      3.5.5
Ring(s), Morita invariants of      3.5.10
Ring(s), Noetherian      0.1.6
Ring(s), of differential operators      15.0.0 ff 15.5.1
Ring(s), of Morita context      1.1.6
Ring(s), PI      13.0.0 ff 13.1.6
Ring(s), pri-----      0.1.8
Ring(s), prime      0.2.3
Ring(s), primitive      0.3.2
Ring(s), principal ideal      0.1.8
Ring(s), quotient      2.1.3 3.1.1
Ring(s), regular      7.7.1
Ring(s), semiprime      0.2.7
Ring(s), semiprimitive      0.3.9
Ring(s), semisimple      0.1.11
Ring(s), simple      0.1.10
Ring(s), skew Laurent polynomial      1.4.3
Ring(s), skew Laurent power series      1.4.4
Ring(s), skew polynomial      1.2.4
Ring(s), skew power series      1.4.1
Ring(s), trace      13.9.2 13.9.4
Ring(s), weakly ideal invariant      6.8.13
Saturated chain      13.10.13
Schanuel’s Lemma      7.1.2
Schanuel’s lemma, long      7.1.2
Schelter’s theorem      13.10.12
Schur’s lemma      0.1.9
Second layer, condition      4.3.12
Second layer, link      4.3.7
Semi-invariants      14.1.15
Semicentre      14.4.6
Semidirect product of groups      1.5.7
Semiprime ideal      0.2.7
Semiprime ring      0.2.7
Semiprimitive ideal      0.3.9
Semiprimitive polynomial ring      13.2.7
Semiprimitive ring      0.3.9
Semirnaximal      5.8.5
Semisimple action      14.1.12
Semisimple Lie algebra      14.1.12
Semisimple module      0.1.2
Semisimple ring      0.1.11
Semistable      6.9.8
Serre, conjecture      11.8.0
Serre, theorem      11.7.4 11.7.13
Simple module      0.1.2
Simple module, endomorphism ring of      9.0.0 ff
Simple ring      0.1.10
Simple ring, $A_n'(k)$ being      1.8.6
Simple ring, $B_n(k)$ being      1.3.9
Simple ring, $K_0$ of      12.7.1 ff
Simple ring, $P_{\lambda}(k)$ being      1.8.7
Simple ring, $\mathcal{A}(V,\delta,\Gamma)$ being      14.8.9
Simple ring, and enveloping algebras      14.3.6 14.3.7
Simple ring, being Dedekind domain      7.11.1 ff
Simple ring, being pri-ring      11.2.13
Simple ring, bounds on generators in      6.7.8
Simple ring, centre of      2.1.16
Simple ring, cyclic module over      5.7.3
Simple ring, derivation ring being      15.3.8
Simple ring, examples of      1.8.1 ff 1.9.8 7.8.14
Simple ring, GK dimension of      8.3.19
Simple ring, global dimension of      7.5.5
Simple ring, ideals in tensor product of      9.6.9
Simple ring, Krull dimension of      6.6.7 6.6.11 6.9.24 8.3.19
Simple ring, not being $\sim$ domain      12.7.16
Simple ring, not being matrix ring      12.7.7 ff
Simple ring, polynomials over      6.7.9
Simple ring, projective modules over      11.7.14
Simple ring, skew group ring being      7.8.12
Simple ring, Weyl algebra being      1.3.5
Singular ideal      2.2.4
Singular ideal, $\mathcal{F}$-      10.3.5
Singular ideal, being nilpotent      2.3.4
Skew enveloping algebra      see “Enveloping algebra”
Skew group ring      see “Group ring”
Skew Laurent polynomial ring      see “Skew polynomial ring”
Skew Laurent power series ring      1.4.4
Skew polynomial ring (Laurent)      1.2.1 ff 1.4.1
Skew polynomial ring (Laurent), $K_0$ of      12.5.1 ff 12.6.1
Skew polynomial ring (Laurent), and derivation ring      15.3.2
Skew polynomial ring (Laurent), being integral domain      1.2.9 1.4.5
Skew polynomial ring (Laurent), being Noetherian      1.2.9 1.4.5
Skew polynomial ring (Laurent), being non-Noetherian      1.2.11
Skew polynomial ring (Laurent), being pri-ring      11.2.13
Skew polynomial ring (Laurent), being prime      1.2.9 1.4.5
Skew polynomial ring (Laurent), being regular      7.7.5
Skew polynomial ring (Laurent), being simple      1.8.4 1.8.5
Skew polynomial ring (Laurent), GK dimension of      8.2.11 8.2.15 8.2.16
Skew polynomial ring (Laurent), global dimension of      7.5.3 7.9.1 7.10.1 9.1.14
Skew polynomial ring (Laurent), having projectives stably free      12.3.3
Skew polynomial ring (Laurent), in several variables      1.6.1 ff
Skew polynomial ring (Laurent), incomparability in      14.2.9
Skew polynomial ring (Laurent), Krull dimension of      6.5.4 6.6.6 6.6.10 6.9.1 9.1.14
Skew polynomial ring (Laurent), leading ideals of      1.2.9 1.8.5
Skew polynomial ring (Laurent), over commutative rings      6.9.1 ff
Skew polynomial ring (Laurent), primes of      10.6.1 ff
Skew polynomial ring (Laurent), stably free ideals of      11.2.7 11.2.8
Skew polynomial ring (Laurent), universal property of      1.2.5
Skew power series ring      1.4.1
Skew power series ring, global dimension of      7.5.3
sl(2,k), dimensions of enveloping algebra of      8.5.12 ff
Small’s theorem      4.1.4
Smash product      1.9.7
Socle      6.2.14
Socle, Krull      6.2.14
Socle, Krull-sequence      6.2.14
Solvable Lie algebra      6.6.2 14.1.7
Somewhat commutative      8.6.9
Somewhat commutative, derivation ring being      15.1.21
sparse      4.6.11
Spectrum, $\sigma-$      10.6.3
Spectrum, J      11.6.6
Spectrum, prime      0.2.3
Splitting field      13.3.6
Stability      11.0.0 ff
Stable g-      14.2.4
Stable G-----      10.5.4
Stable generation      6.7.1 ff 11.6.11
Stable ideal      1.8.2
Stable identity      13.1.16
Stable isomorphism      12.1.4
Stable matrix      11.5.16
Stable range of module      6.7.2
Stable rank      11.3.4
Stable unimodular row      11.3.2
Stably free      11.1.1 11.2.1
Stably free-graded      12.2.10
Stably isomorphic      12.1.4
Standard filtration      1.6.2 7.6.7 8.1.9
Standard matrix units      2.2.11
Standard monomials      1.7.5
State space      12.8.1
Strict      7.6.12
Strongly nilpotent element      0.2.5
Structure of semiprime Goldie rings      3.0.0 ff
Subisomorphic      3.3.4
Symmetric $\delta$-algebra      14.8.3
Symmetric algebra      15.1.18
Syzygy theorem      12.3.1 ff
Topology, patch      4.6.14
Topology, Zariski      4.6.14
Tor      7.1.10
Torsion, $\alpha-$      6.2.18
Torsion, free      3.4.2
Torsion, less      3.4.2
Torsion, module      2.1.17
Torsion, theory      2.4.1
Torsion, with respect to      4.3.2
Torsion, |G|-free      10.5.9
Trace, function      12.7.13
Trace, ideal      10.5.16
Trace, of group ring      7.8.6
Trace, of ring      12.7.13
Trace, proper      12.7.13
Trace, ring      13.9.2 13.9.4
Trace, universal function      12.7.13
Translate of filtration      8.6.14
Translate of grading      7.6.2
Triangular matrix ring      0.1.4
Triangular matrix ring, chain conditions in      1.1.4 1.1.9 1.1.10
Triangular matrix ring, global dimension of      7.5.1
Uniform, dimension      2.2.10
Uniform, module      2.2.5
Uniform, right ideals      3.3.2 ff
Unimodular, row/column      11.1.8
Unimodular, stable row/column      11.3.2
Universal enveloping algebra      see “Enveloping algebra”
Unstable      6.9.8
Weak algorithm      11.3.9
Weak dimension      7.1.4
Weak global dimension      7.1.9
Weight(s), Jordan — Holder      14.4.10
Weight(s), space      14.1.19
Weyl algebra ($A_n$, $A'_n$, $B_n$)      1.3.1 ff
Weyl algebra ($A_n$, $A'_n$, $B_n$), $A'_n$      1.8.6
Weyl algebra ($A_n$, $A'_n$, $B_n$), $B_n$      1.3.9
Weyl algebra ($A_n$, $A'_n$, $B_n$), $D_n$      6.6.18
Weyl algebra ($A_n$, $A'_n$, $B_n$), $K_0$ of      12.1.6 12.3.3
Weyl algebra ($A_n$, $A'_n$, $B_n$), $K_0$ of overringof      12.3.3 12.6.14 12.7.7
Weyl algebra ($A_n$, $A'_n$, $B_n$), and $\mathcal{A}(V,\delta,\Gamma)$      14.8.1 ff
Weyl algebra ($A_n$, $A'_n$, $B_n$), and algebraic g      14.7.1 ff
Weyl algebra ($A_n$, $A'_n$, $B_n$), and Nullstellensatz      9.1.8 9.4.22
Weyl algebra ($A_n$, $A'_n$, $B_n$), and solvable g      14.9.1 ff
Weyl algebra ($A_n$, $A'_n$, $B_n$), as derivation ring      15.1.5
Weyl algebra ($A_n$, $A'_n$, $B_n$), as differential operators      1.3.6
Weyl algebra ($A_n$, $A'_n$, $B_n$), as factor of enveloping algebra      14.6.1 ff
Weyl algebra ($A_n$, $A'_n$, $B_n$), being almost commutative      8.4.3
Weyl algebra ($A_n$, $A'_n$, $B_n$), being Dedekind      5.2.11 7.11.3
Weyl algebra ($A_n$, $A'_n$, $B_n$), being maximal order      5.1.6
Weyl algebra ($A_n$, $A'_n$, $B_n$), being not a principal ideal ring      7.11.8
Weyl algebra ($A_n$, $A'_n$, $B_n$), being simple Noetherian domain      1.3.5 1.3.8 1.8.6
Weyl algebra ($A_n$, $A'_n$, $B_n$), embeddings of      6.6.19
Weyl algebra ($A_n$, $A'_n$, $B_n$), general linear rank of first      11.1.16
Weyl algebra ($A_n$, $A'_n$, $B_n$), generators of right ideals of      6.7.8
Weyl algebra ($A_n$, $A'_n$, $B_n$), GK dimension of      8.1.15 8.2.7
Weyl algebra ($A_n$, $A'_n$, $B_n$), GK dimension of modules over      8.5.3 ff
Weyl algebra ($A_n$, $A'_n$, $B_n$), global dimension of      7.5.8
Weyl algebra ($A_n$, $A'_n$, $B_n$), global dimension of overrings of      9.1.12 9.4.23
Weyl algebra ($A_n$, $A'_n$, $B_n$), has finite endomorphism rings      9.5.5 9.7.5
Weyl algebra ($A_n$, $A'_n$, $B_n$), has projectives stably free      12.3.3
Weyl algebra ($A_n$, $A'_n$, $B_n$), has stably free ideals      11.1.4 11.2.11
Weyl algebra ($A_n$, $A'_n$, $B_n$), in derivation ring      15.2.6 15.3.2
Weyl algebra ($A_n$, $A'_n$, $B_n$), Krull dimension of      6.5.8 6.5.10 6.6.15 7.5.9
Weyl algebra ($A_n$, $A'_n$, $B_n$), Krull dimension of overrings of      9.1.12 9.4.23
Weyl algebra ($A_n$, $A'_n$, $B_n$), matrices over      7.11.7
Weyl algebra ($A_n$, $A'_n$, $B_n$), modules over      5.7.18
Weyl algebra ($A_n$, $A'_n$, $B_n$), over $\mathbb{Z}$      4.6.13 11.7.8
Weyl algebra ($A_n$, $A'_n$, $B_n$), quotient division ring of      6.6.18 9.6.12
Weyl algebra ($A_n$, $A'_n$, $B_n$), skew group ring over      7.8.14 12.7.7
Weyl algebra ($A_n$, $A'_n$, $B_n$), stable range of      11.2.15
Word      1.6.2
Zariski topology      4.6.14
Zariski — Lipman conjecture      15.6.3
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