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Approximations and Endomorphism Algebras of Modules : Volume 1 - Approximations /

This monograph- now in its second revised and extended edition- provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatoric...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Trlifaj, Jan
Otros Autores: Göbel, Rüdiger
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin : De Gruyter, 2012.
Edición:2nd ed.
Colección:De Gruyter expositions in mathematics.
Temas:
Acceso en línea:Texto completo

MARC

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049 |a UAMI 
100 1 |a Trlifaj, Jan. 
245 1 0 |a Approximations and Endomorphism Algebras of Modules :  |b Volume 1 - Approximations /  |c Volume 2 - Predictions. 
250 |a 2nd ed. 
260 |a Berlin :  |b De Gruyter,  |c 2012. 
300 |a 1 online resource (1002 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a De Gruyter Expositions in Mathematics ;  |v v. 41 
520 |a This monograph- now in its second revised and extended edition- provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatorics and model theory. The book starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory. 
588 0 |a Print version record. 
505 8 |a 4 Slender modules4.1 Factors of products and slender modules; 4.2 Slender modules over Dedekind domains; 4.3 Open problems; PART II: APPROXIMATIONS AND COTORSION PAIRS ; 5 Approximations of modules; 5.1 Preenvelopes and precovers; 5.2 Cotorsion pairs and Tor-pairs; 5.3 Minimal approximations; 5.4 Open problems; 6 Complete cotorsion pairs; 6.1 Ext and direct limits; 6.2 The abundance of complete cotorsion pairs; 6.3 Ext and inverse limits; 6.4 Open problems; 7 Hill lemma and its applications; 7.1 The general version of the Hill Lemma; 7.2 Kaplansky theorem for cotorsion pairs. 
505 8 |a 7.3 C-socle sequences and Filt.(C)-precovers7.4 Singular compactness for C-filtered modules; 7.5 Ascending and descending properties of modules; 7.6 The rank version of the Hill Lemma; 7.7 Matlis cotorsion and strongly flat modules; 7.8 Open problems; 8 Deconstruction of the roots of Ext; 8.1 Approximations by modules of finite homological dimensions; 8.2 Closure properties providing for deconstruction; 8.3 The closure of a cotorsion pair; 9 Modules of projective dimension one; 9.1 Structure of P 1 and WI for semiprime Goldie rings; 9.2 The class lim P 1; 9.3 Open problems. 
505 8 |a 10 Kaplansky classes and abstract elementary classes10.1 Kaplansky classes and deconstructibility; 10.2 Flat Mittag-Leffler modules revisited; 10.3 Abstract elementary classes of the roots of Ext; 10.4 Open problems; 11 Independence results for cotorsion pairs; 11.1 Completeness of cotorsion pairs under the Diamond Principle; 11.2 Uniformisation and cotorsion pairs not generated by a set; 11.3 Open problems; 12 The lattice of cotorsion pairs; 12.1 Ultra-cotorsion-free modules and the Strong Black Box; 12.2 Rational cotorsion pairs; 12.3 Embedding posets into the lattice of cotorsion pairs. 
505 8 |a PART III: TILTING AND COTILTING APPROXIMATIONS 13 Tilting approximations; 13.1 Tilting modules; 13.2 Classes of finite type; 13.3 Localisation of tilting modules; 13.4 Product-completeness of tilting modules; 13.5 Open problems; 14 1-tilting modules and their applications; 14.1 Tilting torsion classes; 14.2 The structure of 1-tilting modules and classes over particular rings; 14.3 Baer modules; 14.4 Matlis localisations; 14.5 Open problems; 15 Cotilting classes; 15.1 Cotilting classes and the classes of cofinite type; 15.2 1-cotilting modules and cotilting torsion-free classes. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Modules (Algebra) 
650 0 |a Moduli theory. 
650 0 |a Approximation theory. 
650 6 |a Modules (Algèbre) 
650 6 |a Théorie des modules. 
650 6 |a Théorie de l'approximation. 
650 7 |a Approximation theory  |2 fast 
650 7 |a Modules (Algebra)  |2 fast 
650 7 |a Moduli theory  |2 fast 
700 1 |a Göbel, Rüdiger. 
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776 0 8 |i Print version:  |z 9783110218107 
830 0 |a De Gruyter expositions in mathematics. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=893905  |z Texto completo 
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