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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.
Last update: T_KA (14.05.2013)
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Předmět je zakončen ústní zkouškou. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (10.06.2019)
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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.
Last update: Trlifaj Jan, prof. RNDr., CSc., DSc. (14.12.2023)
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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. Last update: Trlifaj Jan, prof. RNDr., CSc., DSc. (14.12.2023)
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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.
Last update: Trlifaj Jan, prof. RNDr., CSc., DSc. (14.12.2023)
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