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Course, academic year 2017/2018
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Approximations of Modules - NMAG531
Czech title: Aproximace modulů
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Trlifaj, CSc., DSc.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG077
Interchangeability : NALG077
Annotation -
Last update: T_KA (14.05.2013)

An introduction to the theory of envelopes and covers of modules. Complete cotorsion pairs. The proof of the Flat Cover Conjecture. Tilting approximations. Connections to the Finitistic Dimension Conjectures for algebras. Solution to the Baer Problem.
Literature - Czech
Last update: prof. RNDr. Jan Trlifaj, CSc., DSc. (05.10.2017)

R. Göbel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, GEM 41, 2nd rev. ext. ed., Walter de Gruyter, Berlin 2012.

Requirements to the exam -
Last update: prof. RNDr. Jan Trlifaj, CSc., DSc. (05.10.2017)

The exam is oral. Knowledge of selected parts of the monograph Goebel-Trlifaj: Approximations and Endomorphism Algebras of Modules, 2nd rev. ext. ed., Vol. 1, W. de Gruyter, Berlin 2012.

Syllabus -
Last update: T_KA (14.05.2013)

1. An introduction to the theory of envelopes and covers of modules.

2. Complete cotorsion pairs.

3. The proof of the Flat Cover Conjecture.

4. Tilting approximations, finite type.

5. Connections to the Finitistic Dimension Conjectures for algebras.

6. Solution to the Baer Problem.

 
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