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Approximations of Modules - NMAG531

Title:	Aproximace modulů
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015 to 2019
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English
Teaching methods:	full-time
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
Is interchangeable with:	NALG077

Opinion survey results Examination dates Schedule Noticeboard

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, Walter de Gruyter, Berlin 2006.

Syllabus -

Last update: prof. RNDr. Jan Trlifaj, CSc., DSc. (14.12.2023)

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.