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Course, academic year 2017/2018
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Algebra II - NMAI063
Czech title: Algebra II
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017 to 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://msekce.karlin.mff.cuni.cz/~zemlicka/
Guarantor: doc. Mgr. et Mgr. Jan Žemlička, Ph.D.
Class: Informatika Bc.
Classification: Mathematics > Algebra
Co-requisite : NMAI062
Incompatibility : NALG027
Annotation -
Last update: T_KA (17.05.2010)

The second part of course in basic algebra is concerned with divisibilty in commmutative domains, extensions of fields and basic properties of the notion variety.
Literature -
Last update: RNDr. Alexandr Kazda, Ph.D. (18.02.2018)

S. Lang. Algebra, 3rd ed. New York 2002, Springer.

S. MacLane, G. Birkhoff. Algebra 3rd ed, Providence 1999, AMS Chelsea publishing company.

Stanley N. Burris, H.P. Sankappanavar. A Course in Universal Algebra, The Millenium Edition, Waterloo 2012. URL: https://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html

Requirements to the exam -
Last update: RNDr. Alexandr Kazda, Ph.D. (18.02.2018)

Oral examination covering all the material in the assigned reading.

Syllabus -
Last update: RNDr. Alexandr Kazda, Ph.D. (19.02.2018)

1. Divisibility in commutative cancellative monoids.

2. Principal ideal and Euclidean domains. Polynomial rings, multiplicity of roots, evaluation homomorphism. Why all finite multiplicative subgroups of fields are cyclic.

3. Splitting fields of a polynomial. Rupture field of a polynomial.

4. Finite fields. Existence of irreducible polynomials over finite fields.

5. Free algebras, terms and varieties.

 
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