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Lifting Modules: Supplements and Projectivity in Module Theory 2006 ed. [Pehme köide]

(Universitat Dusseldorf, Germany), (University of Otago, New Zealand), , (Universidade di Porto, Portugal)
  • Formaat: Paperback, 394 pages, kõrgus x laius x paksus: 240x168x21 mm, kaal: 696 g, XIII, 394 p.
  • Sari: Frontiers in Mathematics
  • Ilmumisaeg: 18-Jul-2006
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3764375728
  • ISBN-13: 9783764375720
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  • Formaat: Paperback, 394 pages, kõrgus x laius x paksus: 240x168x21 mm, kaal: 696 g, XIII, 394 p.
  • Sari: Frontiers in Mathematics
  • Ilmumisaeg: 18-Jul-2006
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3764375728
  • ISBN-13: 9783764375720
Teised raamatud teemal:
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.The text begins with an introduction to small submodules, the radical, variations on projectivity, and hollow dimension. The subsequent chapters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange property and local semi-T-nilpotency), supplements in modules (with specific emphasis on semilocal endomorphism rings), finishing with a long chapter on lifting modules, leading up their use in the theory of perfect rings, Harada rings, andquasi-Frobenius rings.Most of the material in the monograph appears in book form for the first time. The main text is augmented by a plentiful supply of exercises together with comments on further related material and on how the theory has evolved.

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.
Preface vii
Introduction ix
Notation xiii
Basic notions
1(54)
Preliminaries
1(10)
Small submodules and the radical
11(9)
Cosmall inclusions and coclosed submodules
20(6)
Projectivity conditions
26(21)
Hollow dimension of modules
47(8)
Preradicals and torsion theories
55(48)
Preradicals and colocalisation
55(15)
Torsion theories
70(4)
Torsion theories related to small modules
74(10)
Corational modules
84(10)
Proper classes and τ-supplements
94(9)
Decompositions of modules
103(104)
The exchange property
103(21)
LE-modules and local semi-T-nilpotency
124(18)
Local direct summands
142(20)
The total and LE-decompositions
162(18)
Stable range 1 and cancellation
180(14)
Decomposition uniqueness and biuniformity
194(13)
Supplements in modules
207(58)
Semilocal and weakly supplemented modules
207(11)
Weak supplements and hollow dimension
218(9)
Semilocal endomorphism rings
227(6)
Supplemented modules
233(24)
Submodules with unique coclosure
257(8)
From lifting to perfect modules
265(94)
Lifting modules
265(12)
Finite direct sums of lifting modules
277(12)
The lifting property for infinite sums
289(7)
σ-lifting modules
296(11)
Semi-discrete and quasi-discrete modules
307(10)
Discrete and perfect modules
317(14)
Injective modules lifting in σ[ M]
331(16)
Extending modules lifting in σ[ M]
347(12)
Appendix
359(4)
Hall's Marriage Theorem
359(3)
Konig's Graph Theorem
362(1)
Bibliography 363(24)
Index 387


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