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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
Teaching methods:	full-time

Guarantor:	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 -

Last update: T_KA (14.05.2013)

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.

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)

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.

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: "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.

Syllabus -

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

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.

Entry requirements -

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

Basics of module theory and set theory.