1.
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図書
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Jacob Barshay
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2.
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図書
|
Louis H. Rowen
目次情報:
続きを見る
Introduction: An Overview of Ring Theory |
Table of Principal Notation |
General Fundamentals |
Construction of Rings |
Basic Structure Theory |
Rings of Fractions and Embedding Theorems |
Categorical Aspects of Module Theory |
Homology and Cohomology |
Rings with Polynomial Identities and Affine Algebras |
Central Simple Algebras |
Rings from Representation Theory |
Dimensions for Modules and Rings |
Major Theorems and Counterexamples for Volume II |
References |
Index of References According to Section |
Cumulative Subject Index for Volumes I and II |
Index |
Introduction: An Overview of Ring Theory |
Table of Principal Notation |
General Fundamentals |
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3.
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図書
|
I. Reiner
出版情報: |
London ; New York : Academic Press, 1975 xii, 395 p. ; 24 cm |
シリーズ名: |
L.M.S. monographs ; 5 |
子書誌情報: |
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目次情報:
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Foreword |
Preface |
Acknowledgements |
Permanent notation |
Algebraic preliminaries / 1: |
Integral closure |
Homological algebra / 2: |
Localization / 3: |
Dedekind domains / 4: |
Completions and valuations / 5: |
Radicals of rings / 6: |
Semisimple rings and simple algebras / 7: |
Orders |
Definitions and examples / 8: |
Reduced norms and traces / 9: |
Existence of maximal orders; discriminants / 10: |
Localization of orders / 11: |
Maximal orders in skewfields (local case) |
Uniqueness of maximal orders / 12: |
Ramification index; inertial degree / 13: |
Finite residue class field case / 14: |
Morita equivalence |
Progenerators / 15: |
Morita correspondence / 16: |
Maximal orders over discrete valuation rings |
Maximal orders (complete local case) / 17: |
Maximal orders (local case) / 18: |
Ideals / 19: |
Different, discriminant / 20: |
Maximal orders over Dedekind domains |
Basic results / 21: |
Ideal theory / 22: |
Alternate approach to global ideal theory / 23: |
Norms of ideals / 24: |
Ideal classes; Jordan-Zassenhaus theorem / 25: |
Genus / 27: |
Crossed-product algebras |
Brauer groups / 28: |
Cyclic algebras / 29: |
Cyclic algebras over local fields / 31: |
Simple algebras over global fields |
Splitting of simple algebras / 32: |
Reduced norms / 33: |
Eichler's Theorem / 34: |
Ideal class groups / 35: |
K[subscript 0] of maximal orders / 36: |
Picard groups / 37: |
Non-maximal orders / 38: |
Hereditary orders |
Local theory of hereditary orders / 39: |
Global theory of hereditary orders / 40: |
Group rings / 41: |
References |
Index |
Foreword |
Preface |
Acknowledgements |
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4.
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図書
|
J.-E. Björk
出版情報: |
Amsterdam : North-Holland. , New York : sole distributors for the U.S.A. and Canada, Elsevier North-Holland., 1979 xvii, 374 p. ; 23 cm |
シリーズ名: |
North-Holland mathematical library ; v. 21 |
子書誌情報: |
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5.
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図書
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A.J. Berrick & M.E. Keating
目次情報:
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Basics / 1: |
Direct sums and their short exact sequences / 2: |
Noetherian rings and polynomial rings / 3: |
Artinian rings and modules / 4: |
Dedekind domains / 5: |
Modules over Dedekind domains / 6: |
Basics / 1: |
Direct sums and their short exact sequences / 2: |
Noetherian rings and polynomial rings / 3: |
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6.
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図書
|
Askar Tuganbaev
目次情報:
続きを見る
Projective and Injective Modules / 1: |
Bezout and Regular Modules / 2: |
Continuous and Finite-Dimensional Modules / 3: |
Classical Localizations / 4: |
Flat Modules and Semiperfect Rings / 5: |
Semihereditary Rings / 6: |
Endomorphism Rings and Distributivity / 7: |
Q max (A) and Nonsingular Rings / 8: |
Polynomials, Series and Quaternions / 9: |
Semidistributive Rings and Modules / 10: |
Distributive Group and Monoid Rings / 11: |
Rings Related to Commutative Rings |
Self-injective and Skew-injective Rings / 12: |
Projective and Injective Modules / 1: |
Bezout and Regular Modules / 2: |
Continuous and Finite-Dimensional Modules / 3: |
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7.
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図書
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by Askar A. Tuganbaev
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8.
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図書
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T.Y. Lam
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9.
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図書
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Claudio Procesi
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10.
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図書
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Pascual Jara, Alain Verschoren and Conchi Vidala
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11.
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図書
|
edited by X.H. Cao ... [et al.]
目次情報:
続きを見る
Structure of Finite Groups / Zhongmu Chen ; Wujie Shi ; Guiyen Chen |
The Representation and Cohomology Theory of Modular Lie Algebras / Sen Chiu |
Valuation Theory and Generalizations of Hilbert's 17th Problem / Zhizhong Dai |
Guangxing Zeng Modules over Hyperfinite Groups / Z. Y. Duan |
Pointed Groups and Nilpotent Blocks, Yun Fan Near-Rings in China / Yuen Fong |
The Theory of Formations / Wenbin Guo |
Some Recent Developments in Filtered Ring and Graded Ring Theory in China / Huishi Li Liu |
Structure of Finite Groups / Zhongmu Chen ; Wujie Shi ; Guiyen Chen |
The Representation and Cohomology Theory of Modular Lie Algebras / Sen Chiu |
Valuation Theory and Generalizations of Hilbert's 17th Problem / Zhizhong Dai |
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12.
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図書
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T.Y. Lam
目次情報:
続きを見る
Preface |
Notes to the Reader |
Wedderburn-Artin Theory |
Jacobson Radical Theory |
Introduction to Representation Theory |
Prime and Primitive Rings |
Introduction to Division Rings |
Ordered Structures in Rings |
Local Rings, Semilocal Rings, and Idempotents, Perfect and Semiperfect Rings |
Name Index |
Subject Index |
Preface |
Notes to the Reader |
Wedderburn-Artin Theory |
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13.
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図書
|
A. Borel ... [et al.]
目次情報:
続きを見る
Categories Derivees et Foncteurs Derives / P.-P Grivel |
Coherent D-Modules / B. Kaup |
Local Theory of Meromorphic Connections in Dimension One (Fuchs Theory) / A. Haefliger |
Regular Connections' After Deligne / B. Malgrange |
The Weyl Algebra / F. Ehlers |
Operations on Algebraic D-Modules / A. Borel |
Coherent, Holonomic and Regular Holonomic Complexes |
The Riemann-Hilbert Correspondence |
References |
Categories Derivees et Foncteurs Derives / P.-P Grivel |
Coherent D-Modules / B. Kaup |
Local Theory of Meromorphic Connections in Dimension One (Fuchs Theory) / A. Haefliger |
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14.
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図書
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by Constantin Năstăsescu and Freddy van Oystaeyen
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15.
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図書
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Robert Wisbauer
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16.
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図書
|
Donald S. Passman
目次情報:
続きを見る
Projective modules: Modules and homomorphisms Projective modules |
Completely reducible modules Wedderburn rings Artinian rings Hereditary rings |
Dedekind domains Projective dimension Tensor products Local rings |
Polynomial rings: Skew polynomial rings Grothendieck groups |
Graded rings and modules Induced modules Syzygy theorem Patching theorem |
Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules |
Injective dimension Essential extensions Maximal ring of quotients |
Classical ring of quotients Goldie rings |
Uniform dimension |
Uniform injective modules Reduced rank |
Index |
Projective modules: Modules and homomorphisms Projective modules |
Completely reducible modules Wedderburn rings Artinian rings Hereditary rings |
Dedekind domains Projective dimension Tensor products Local rings |
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17.
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図書
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Jonathan S. Golan, Tom Head
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18.
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図書
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Carl Faith
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19.
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図書
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by Robert L. Kruse and David T. Price
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20.
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図書
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[by] Neal H. McCoy
出版情報: |
Bronx, N.Y. : Chelsea Pub. Co., [1973] x, 161 p. ; 24 cm |
子書誌情報: |
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21.
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図書
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N. Popescu
出版情報: |
London ; New York : Academic Press, 1973 xii, 467 p. ; 24 cm |
シリーズ名: |
L.M.S. monographs ; 3 |
子書誌情報: |
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22.
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図書
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W. Borho, J.-L. Brylinski, R. MacPherson
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23.
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図書
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Irving Kaplansky
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24.
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図書
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Leonard Gillman, Meyer Jerison
|
25.
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図書
|
Gregory Karpilovsky
出版情報: |
Oxford [Oxfordshire] : Clarendon Press , New York : Oxford University Press, 1988 xiv, 370 p. ; 24 cm |
シリーズ名: |
Oxford science publications |
子書誌情報: |
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目次情報:
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Introduction / 1: |
Algebraic Units / 2: |
The Unit Group of ... / 3: |
Multiplicative Groups of Fields / 4: |
Multiplicative Groups of Division Rings / 5: |
Rings with Cyclic Unit Groups / 6: |
Finite Generation of Unit Groups / 7: |
Unit Groups of Group Rings / 8: |
Introduction / 1: |
Algebraic Units / 2: |
The Unit Group of ... / 3: |
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26.
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図書
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Paulo Ribenboim
|
27.
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図書
|
Irving Kaplansky
|
28.
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図書
|
D.G. Northcott
出版情報: |
Cambridge : Cambridge University Press, 1968 xiv, 444 p. ; 24 cm |
子書誌情報: |
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目次情報:
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Preface |
Some notes for the reader |
Introduction to some basic ideas / 1: |
Prime ideals and primary submodules / 2: |
Rings and modules of fractions / 3: |
Noetherian rings and modules / 4: |
The theory of grade / 5: |
Hilbert rings and the Zeros Theorem / 6: |
Multiplicity theory / 7: |
The Koszul complex / 8: |
Filtered rings and modules / 9: |
Index |
Preface |
Some notes for the reader |
Introduction to some basic ideas / 1: |
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29.
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図書
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Neal H. McCoy
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30.
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図書
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L.A. Skornyakov
出版情報: |
Edinburgh : Oliver & Boyd, 1964 viii, 182 p. ; 23 cm |
子書誌情報: |
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31.
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図書
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J.L. Bueso, P. Jara, A. Verschoren
目次情報:
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Localization |
Extensions |
Stability |
Compatibility and sheaves |
Localization |
Extensions |
Stability |
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32.
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図書
|
John Dauns
出版情報: |
Cambridge, England ; New York : Cambridge University Press, 1994 xviii, 442 p. ; 24 cm |
子書誌情報: |
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目次情報:
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Modules / 1: |
Free modules / 2: |
Injective modules / 3: |
Tensor products / 4: |
Certain important algebras / 5: |
Simple modules and primitive rings / 6: |
The Jacobson radical / 7: |
Subdirect product decompositions / 8: |
Primes and semiprimes / 9: |
Projective modules and more on Wedderburn theorems / 10: |
Direct sum decompositions / 11: |
Simple algebras / 12: |
Hereditary rings, free and projective modules / 13: |
Module constructions / 14: |
Categories and functors / 15: |
Module categories / 16: |
Flat modules / 17: |
Purity / 18: |
Modules / 1: |
Free modules / 2: |
Injective modules / 3: |
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33.
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図書
|
by Askar A. Tuganbaev
目次情報:
続きを見る
Preface |
Symbols |
Some Basic Facts of Ring Theory / 1: |
Preliminaries / 1.: |
Finiteness Conditions and the Jacobson Radical / 2.: |
Semiprime and Reduced Rings / 3.: |
Series and Polynomials / 4.: |
Rings of Quotients / 5.: |
Regular and Strongly Regular Rings / 2: |
Regular Modules and Rings / 6.: |
Biregular and Strongly Regular Rings / 7.: |
Modules over Regular Rings / 8.: |
Regular Group Rings / 9.: |
Regular Laurent Series Rings / 10.: |
Pierce Stalks of Regular Rings / 11.: |
Regular Quaternion Algebras / 12.: |
Rings of Bounded Index and I[subscript 0]-rings / 3: |
Nonsingular and Finite-dimensional Rings / 13.: |
Rings of Bounded Index / 14.: |
I[subscript 0]-rings / 15.: |
Semiperfect Rings / 16.: |
Semiregular and Weakly Regular Rings / 4: |
Semiregular Modules / 18.: |
Semiregular Rings and Continuous Modules / 19.: |
Weakly Regular Rings / 20.: |
Semi-Artinian and Perfect Rings / 21.: |
V-rings / 22.: |
Max Rings and [pi]-regular Rings / 5: |
Strongly [pi]-regular Rings / 23.: |
[pi]-regular Rings of Bounded Index / 24.: |
Distributively Generated Rings / 25.: |
Max Rings / 26.: |
Max Rings and Rings of Quotients / 27.: |
Exchange Rings and Modules / 6: |
Exchange Modules / 28.: |
Exchange Rings / 29.: |
Rings of Stable Range One / 30.: |
Continuous and Quasi-projective Modules / 31.: |
Pierce Stalks of Exchange Rings / 32.: |
Pure-injective Modules / 33.: |
Separative Exchange Rings / 7: |
Separativity, Strong Separativity, and Refinement Monoids / 34.: |
Stable Range / 35.: |
Diagonalization of Matrices / 36.: |
Separative Regular Rings / 37.: |
K[subscript 1] of Separative Exchange Rings / 38.: |
Bibliography |
Index |
Preface |
Symbols |
Some Basic Facts of Ring Theory / 1: |
|
34.
|
図書
|
edited by Yuri Bahturin
|
35.
|
図書
|
I. Reiner
目次情報:
続きを見る
Foreword |
Preface |
Acknowledgements |
Permanent notation |
Algebraic preliminaries / 1: |
Integral closure |
Homological algebra / 2: |
Localization / 3: |
Dedekind domains / 4: |
Completions and valuations / 5: |
Radicals of rings / 6: |
Semisimple rings and simple algebras / 7: |
Orders |
Definitions and examples / 8: |
Reduced norms and traces / 9: |
Existence of maximal orders; discriminants / 10: |
Localization of orders / 11: |
Maximal orders in skewfields (local case) |
Uniqueness of maximal orders / 12: |
Ramification index; inertial degree / 13: |
Finite residue class field case / 14: |
Morita equivalence |
Progenerators / 15: |
Morita correspondence / 16: |
Maximal orders over discrete valuation rings |
Maximal orders (complete local case) / 17: |
Maximal orders (local case) / 18: |
Ideals / 19: |
Different, discriminant / 20: |
Maximal orders over Dedekind domains |
Basic results / 21: |
Ideal theory / 22: |
Alternate approach to global ideal theory / 23: |
Norms of ideals / 24: |
Ideal classes; Jordan-Zassenhaus theorem / 25: |
Genus / 27: |
Crossed-product algebras |
Brauer groups / 28: |
Cyclic algebras / 29: |
Cyclic algebras over local fields / 31: |
Simple algebras over global fields |
Splitting of simple algebras / 32: |
Reduced norms / 33: |
Eichler's Theorem / 34: |
Ideal class groups / 35: |
K[subscript 0] of maximal orders / 36: |
Picard groups / 37: |
Non-maximal orders / 38: |
Hereditary orders |
Local theory of hereditary orders / 39: |
Global theory of hereditary orders / 40: |
Group rings / 41: |
References |
Index |
Foreword |
Preface |
Acknowledgements |
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36.
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図書
|
B.J. Gardner, R. Wiegandt
目次情報:
続きを見る
Preface |
Interdependence Chart |
General Fundamentals / Chapter I.: |
Rudiments / 1.1: |
Some elementary ring theory / 1.2: |
Skew polynomial rings / 1.3: |
The General Theory of Radicals / Chapter II.: |
Radical classes / 2.1: |
Radical constructions / 2.2: |
Semisimple classes / 2.3: |
Radical Theory for Associative Rings / Chapter III.: |
Semisimple classes of associative rings / 3.1: |
Hereditary radicals and their semisimple classes / 3.2: |
Lower radical constructions / 3.3: |
The termination of the Kurosh radical construction / 3.4: |
The Sulinski-Anderson-Divinsky problem / 3.5: |
Supernilpotent radicals and their semisimple classes / 3.6: |
Supernilpotent radicals and weakly special classes / 3.7: |
Special radicals / 3.8: |
Supplementing and dual radicals / 3.9: |
Subidempotent radicals / 3.10: |
Hypernilpotent and hypoidempotent radicals / 3.11: |
Partition of simple rings, unequivocal rings / 3.12: |
Minimally embeddable rings / 3.13: |
Modules and radicals / 3.14: |
Radicals defined by means of elements / 3.15: |
One-sided hereditary radicals and stable radicals / 3.16: |
Strong radicals and strict radicals / 3.17: |
Normal radicals / 3.18: |
A-radicals / 3.19: |
Radical semisimple classes / 3.20: |
Concrete Radicals and Structure Theorems / Chapter IV.: |
The principal nil radicals / 4.1: |
Separation of the nil radicals / 4.2: |
Coincidence of the nil radicals / 4.3: |
The Jacobson radical / 4.4: |
Structure theorems for Jacobson semisimple rings / 4.5: |
One-sided primitivity and idempotent simple quasi-regular rings / 4.6: |
Weakly primitive rings / 4.7: |
The Brown-McCoy radical / 4.8: |
Radicals of matrices and polynomials / 4.9: |
Radicals on artinian rings / 4.10: |
Concrete hypernilpotent radicals / 4.11: |
Concrete hypoidempotent radicals / 4.12: |
Special Features of the General Radical Theory / Chapter V.: |
Degeneracy and pathology of nonassociative radical theory / 5.1: |
Sufficient condition for a well-behaved radical theory: Terlikowska-Oslowska's approach / 5.2: |
Sufficient condition for a well-behaved radical theory: Beidar's approach / 5.3: |
On the radical theory of associative rings with involution / 5.4: |
On the radical theory of near-rings / 5.5: |
References |
List of Symbols |
List of Standard Conditions |
Author Index |
Subject Index |
Preface |
Interdependence Chart |
General Fundamentals / Chapter I.: |
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37.
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図書
|
edited by Alberto Facchini, Evan Houston, Luigi Salce
|
38.
|
図書
|
David J. Green
|
39.
|
図書
|
by Jon F. Carlson ... [et al.]
目次情報:
続きを見る
Preface |
Acknowledgements |
Homological Algebra / 1: |
Introduction |
Complexes and Sequences / 2: |
Projective and Injective Models / 3: |
Resolutions / 4: |
Ext / 5: |
Tensor Products and Tor / 6: |
Group Algebras |
Duality and Tensor Products |
Induction and Restriction |
Radicals, Socles and Projective Modules |
Degree Shifting |
The Stable Category |
Group Cohomology and Change of Coefficients / 7: |
Projective Resolutions |
Minimal Resolutions |
The Bar Resolution |
Applications to Low Dimensional Cohomology |
Restrictions, Inflations and Transfers |
Cohomology Products |
Yoneda Splices and Compositions of Chain Maps |
Products and Group Algebras |
Restriction, Inflation and Transfer |
Cohomology Ring Computations |
Shifted Subgroups and Restrictions |
Automorphisms and Cohomology |
Spectral Sequences |
The Spectral Sequence of a Biocomplex |
Products |
The Lyndon-Hochschild-Serre Spectral Sequence |
Extension Classes |
Minimal Resolutions and Convergence |
Exact Couples and the Bockstein Spectral Sequence |
Norms and the Cohomology of Wreath Products |
Wreath Products |
The Norm Map |
Examples and Applications |
Finite Generation of Cohomology |
Steenrod Operations |
The Steenrod Algebra and Modules |
The Steenrod Operations on Cohomology |
Cohomology and Modules Over the Steenrod Algebra |
The Cohomology of Extraspecial 2-Groups |
The Cohomology of Extraspecial p-Groups |
Serre's Theorem on the Vanishing of Bocksteins |
Varieties and Elementary Abelian Subgroups / 8: |
Filtrations on Modules |
Vanishing Products of Cohomology Elements |
Minimal Primes in Cohomology Rings |
The Stratification Theorem |
Cohomology Rings of Modules / 9: |
Generalized Bocksteins Over Elementary Abelian Groups |
Rank Varieties and Cohomology Rings Over Elementary Abelian Groups |
The Cohomological Support Variety of a Module |
Equating the Rank and Cohomological Support Varieties |
The Tensor Product Theorem |
Properties of the Cohomological Support Varieties |
Complexity and Multiple Complexes / 10: |
Notes on Dimension and Rates of Growth |
Complexity of Modules |
Varieties for Modules with Other Coefficient Rings |
Projective Resolutions as Multiple Complexes |
Duality Complexes / 11: |
Gaps in Cohomology |
PoincarF Duality Complexes |
Differentials in the HSS |
Cohen Macaulay Cohomology Rings |
Further Considerations |
Transfers, Depth and Detection / 12: |
Notes on Depth and Associated Primes |
Depth and the p-Rank of the Center |
Varieties and Transfers |
Detection and Depth-Essential Cohomology |
Special Cases |
Associated Primes in Cohomology |
Unstable Modules |
Subgroup Complexes / 13: |
Posets of Subgroups and Cell Complexes |
Homotopy Equivalences and Equivariance |
Complexes of Posets of Finite Groups |
The Bouc Complex |
Applications to Cohomology |
Decompositions of Molecules |
Additional Remarks |
Cohomology Compositions |
Computer Calculations and Completion Tests / 14: |
The Visual Cohomology Ring: Generators and Relations |
Resolutions, Maps and Homogeneous Parameters |
Tests for Completion |
Two Special Cases |
Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64 / J.F. Carlson ; L. Valero-Elizondo ; Mucheng Zhang |
Notation and References / A: |
Groups of Order 8 / B: |
Groups of Order 16 / C: |
Groups of Order 32 / D: |
Groups of Order 64 / E: |
Tables of Krull Dimension and Depth / F: |
Tables of Hilbert/PoincarF Series / G: |
References |
Index |
Preface |
Acknowledgements |
Homological Algebra / 1: |
|
40.
|
図書
|
Andrei V. Kelarev
出版情報: |
Singapore : World Scientific, c2002 xi, 205 p. ; 23 cm |
シリーズ名: |
Series in algebra ; v. 9 |
子書誌情報: |
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41.
|
図書
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George Janelidze, Bodo Pareigis, Walter Tholen, editors
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42.
|
図書
|
Robert R. Colby, Kent R. Fuller
目次情報:
続きを見る
Preface |
Some module theoretic observations / 1: |
Representable equivalences / 2: |
Tilting modules / 3: |
Representable dualities / 4: |
Cotilting / 5: |
Adjoints and category equivalence / A: |
Noetherian serial rings / B: |
Preface |
Some module theoretic observations / 1: |
Representable equivalences / 2: |
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43.
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図書
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Ernst-August Behrens ; translated by Clive Reis
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44.
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図書
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by Leonard Gillman and Meyer Jerison
|
45.
|
図書
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by M.A. Naimark ; translated from the second Russian edition by Leo F. Boron
出版情報: |
Groningen, The Netherlands : Wolters-Noordhoff Pub., c1972 xvi, 598 p. ; 25 cm |
子書誌情報: |
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46.
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図書
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M.F. Atiyah, I.G. MacDonald
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47.
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図書
|
Hyman Bass
|