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Algebra and Infinite Combinatorics - NMAG565

Title:	Algebra a nekonečná kombinatorika
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 [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

Guarantor:	prof. RNDr. Jan Trlifaj, CSc., DSc.
Teacher(s):	prof. RNDr. Jan Trlifaj, CSc., DSc.
Class:	M Mgr. MSTR M Mgr. MSTR > Volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NALG031
Interchangeability :	NALG031
Is interchangeable with:	NALG031

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Annotation -

Application of principles of infinite combinatorics to solving of problems of modern algebra. Application of Diamond and uniformization principles to the solution of the Whitehead problem.

Last update: T_KA (14.05.2013)

Course completion requirements - Czech

Předmět je zakončen ústní zkouškou.

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

Literature - Czech

J. Trlifaj: The Whitehead problem and beyond (Lecture notes for NMAG565), https://www.karlin.mff.cuni.cz/~trlifaj/ANK_5.pdf.

2. P.C.Eklof, A.H.Mekler, Almost-free Modules (Set-theoretic methods), Revised Ed., North-Holland, New York, 2002.

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

Requirements to the exam -

The exam is oral. Knowledge of the lecture notes J. Trlifaj: "The Whitehead problem and beyond", https://www.karlin.mff.cuni.cz/~trlifaj/ANK_5.pdf, or of selected parts of the monograph Eklof-Mekler: "Almost Free Modules" (Elsevier, Amsterdam, 2002), is required.

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

Syllabus -

1. The Whitead problem.

2. Shelah’s Uniformization Principle and the vanishing of Ext.

3. Diamond, weak diamond, and the non-vanishing of Ext.

4. Singular compactness.

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

Entry requirements -

Basics of module theory and set theory.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (17.05.2019)