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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 2016
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
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: T_KA (20.05.2009)

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

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

Syllabus -
Last update: T_KA (17.05.2010)

1. Divisibility in commutative cancellative monoids.

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

3. Rupture and splitting fields of polynomial.

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

5. Free algebras, terms and varieties.

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