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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 2021
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer 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, Czech
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 SS 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.

Course completion requirements - Czech

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Předmět je zakončen ústní zkouškou.

Literature - Czech

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

1. J. Trlifaj, Approximations of modules, Lecture notes for NMAG531, https://www.karlin.mff.cuni.cz/~trlifaj/AM_2.pdf.

2. 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. (14.12.2023)

The exam is oral. Knowledge of the lecture notes J. Trlifaj: "Approximations of modules" (available at https://www.karlin.mff.cuni.cz/~trlifaj/AM_2.pdf), or 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, is required.

Syllabus -

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

1. C-filtrations, Hill Lemma and its consequences.

2. Approximations of modules and complete cotorsion pairs.

3. Modules of bounded homological dimensions.

4. Purity and deconstruction of modules.

5. Minimal approximations, flat covers, and the Enochs Problem.

6. Tilting modules and approximations.

7. Classes of finite type.

8. Finitistic dimension conjectures.