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Course, academic year 2017/2018
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Algebra and Infinite Combinatorics - NMAG565
Czech 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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
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
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.
Literature - Czech
Last update: prof. RNDr. Jan Trlifaj, CSc., DSc. (05.10.2017)

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

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. (05.10.2017)

The exam is oral. Knowledge od selected parts of the monograph Eklof-Mekler: Almost Free Modules (Elsevier, Amsterdam, 2002) is requsted.

Syllabus -
Last update: T_KA (14.05.2013)

1. Extensions of modules, the Ext group, hereditary rings.

2. Non-perfect rings.

3. The solution of the Whitehead problem for countable groups and modules.

4. Diamond and uniformization.

5. Constructions of non-projective Whitehead modules.

6. The solution of the Whitehead problem for regular cardinals.

7. Shelah's compactness theorem and the general solution of the Whitehead problem.

8. New applications in the module theory.

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