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1.

図書

図書
Paul C. Eklof, Alan H. Mekler
出版情報: Amsterdam : Elsevier, 2002  xxi, 597 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 65
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目次情報: 続きを見る
Algebraic Preliminaries / I:
Homomorphisms and extensions / 1:
Direct sums and products / 2:
Linear topologies / 3:
Set Theory / II:
Ordinary set theory
Filters and large cardinals
Ultraproducts
Clubs and stationary sets / 4:
Games and trees / 5:
utri;-systems and partitions / 6:
Slender Modules / III:
Introduction to slenderness
Examples of slender modules and rings
The Lstrok;os-Eda theorem
Almost Free Modules / IV:
Introduction to aleph; 1 free abelian groups / 0:
kgr;-free modules
aleph; 1 -free abelian groups
Compactness results
Pure Injective Modules / V:
Structure theory
Cotorsion groups
More Set Theory / VI:
Prediction Principles
Models of set theory
L, the constructible universe
MA and PFA
PCF theory and I [lgr;]
Almost Free Modules Revisisted (IV, VI) / VII:
aleph; 1 -free abelian groups revisited
kgr;-free modules revisited
kgr;-free abelian groups
Transversals, lgr;-systems and NPT
Reshuffling lgr;-systems / 3A:
Hereditarily separable groups
NPT and the construction of almost free groups
aleph; 1 -Separable Groups (VI, VII.0,1) / VIII:
Constructions and definitions
aleph; 1 -separable groups under Martin's axiom
aleph; 1 -separable groups under PFA
Quotients Of Products Of Z (III, IV, V) / IX:
Perps and products
Countable products of the integers
Uncountable products of the integers
Radicals and large cardinals
Iterated Sums And Products (III) / X:
The Reid class
Types in the Reid class
Topological Methods (X, IV) / XI:
Inverse and direct limits
Completions
Density and dual bases
Groups of continuous functions
Sheaves of abelian groups
An Analysis Of Ext (VII, VIII.1) / XII:
Ext and Diamond
Ext, MA and Proper forcing
Baer modules
The structure of Ext
The structure of Ext when Hom=0
Uniformization (XII) / XIII:
Whitehead groups and uniformization
The basic construction and its applications
The necessity of uniformization
The diversity of Whitehead groups
Monochromatic uniformization and hereditarily separable groups
The Black Box And Endomorphism Rings(V, VI) / XIV:
Introducing the Black Box
Proof of the Black Box
Endomorphism rings of cotorsion-free groups
Endomorphism rings of separable groups
Weak realizability of endomorphism rings and the Kaplansky Test problems
Some Constructions In ZFC (VII, VIII, XIV) / XV:
A rigid aleph; 1 -free group of cardinality aleph; 1
aleph; n -separable groups with the Corner pathology
Absolutely indecomposable modules
The existence of lgr;-separable groups
Cotorsion Theories, Covers And Splitters(IX, XII.1, XIV) / XVI:
Orthogonal classes and splitters
Cotorsion theories
Almost free splitters
The Black Box and Ext
Dual Groups (IX, XI, XIV) / XVII:
Invariants of dual groups
Tree groups
Criteria for being a dual group
Some non-reflexive groups
Dual groups in L
Algebraic Preliminaries / I:
Homomorphisms and extensions / 1:
Direct sums and products / 2:
2.

図書

図書
by Askar A. Tuganbaev
出版情報: Dordrecht ; Boston, Mass. : Kluwer Academic Publishers, c1998  x, 352 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 449
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3.

図書

図書
T.Y. Lam
出版情報: New York : Springer, c1999  xxi, 557 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 189
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4.

図書

図書
Yves André, Francesco Baldassarri
出版情報: Basel ; Boston : Birkhäuser Verlag, c2001  vii, 214 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 189
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5.

図書

図書
Mitsuyasu Hashimoto
出版情報: Cambridge UK : Cambridge University Press, 2000  xvi, 281 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 282
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目次情報: 続きを見る
Introduction
Conventions and terminology
Background Materials / Part I:
From homological algebra / 1:
From Commutative ring theory / 2:
Hopf algebras over an arbitrary base / 3:
From representation theory / 4:
Basics on equivariant modules / 5:
Equivariant Modules / Part II:
Homological aspects of (G, A)-modules
Matijevic-Roberts type theorem
Highest Weight Theory / Part III:
Highest weight theory over a field
Donkin systems
Ringel's theory over a field
Ringel's theory over a commutative ring
Approximations of Equivariant Modules / Part IV:
Approximations of (G, A)-modules
An application to determinantal rings
Bibliography
Index
Glossary.
Introduction
Conventions and terminology
Background Materials / Part I:
6.

図書

図書
László Fuchs, Luigi Salce
出版情報: Providence, RI : American Mathematical Society, c2001  xvi, 613 p.
シリーズ名: Mathematical surveys and monographs ; v. 84
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目次情報: 続きを見る
Commutative domains and their modules
Valuation domains
Prufer domains More non-Noetherian domains
Finitely generated modules
Projectivity and projective dimension
Divisible modules Topology and filtration
Injective modules Uniserial modules Heights, invariants and basic submodules
Polyserial modules RD- and pure-injectivity
Torsion modules Torsion-free modules of finite rank
Infinite rank torsion-free modules
Appendix on set theory
Bibliography Author
Index Subject
Index
Commutative domains and their modules
Valuation domains
Prufer domains More non-Noetherian domains
7.

図書

図書
J. R. García Rozas
出版情報: Boca Raton : Chapman & Hall/CRC Press, c1999  137 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 407
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8.

図書

図書
Askar Tuganbaev
出版情報: Australia : Gordon & Breach, c1999  xv, 258 p. ; 24cm
シリーズ名: Algebra, logic and applications series ; v. 12
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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:
9.

図書

図書
A.J. Berrick, M.E. Keating
出版情報: Cambridge : Cambridge University Press, 2000  xvii, 361 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 67
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Categories / 1:
Categories and exact sequences / 2:
Change of rings / 3:
The Morita theory / 4:
Limits in categories / 5:
Localisation / 6:
Local-global methods / 7:
Categories / 1:
Categories and exact sequences / 2:
Change of rings / 3:
10.

図書

図書
A.J. Berrick & M.E. Keating
出版情報: Cambridge : Cambridge University Press, 2000  xv, 265 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; v. 65
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目次情報: 続きを見る
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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