Algebra II - NALG027
Title: Algebra II
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Trlifaj, CSc., DSc.
Classification: Mathematics > Algebra
Pre-requisite : {Linear Algebra and Geometry}
Co-requisite : NALG026
Interchangeability : NMAG202, NMAI063
Is co-requisite for: NALG008, NALG009, NALG006
Is incompatible with: NMAG202, NMAX063, NUMP007, NMAI063, NMUE004, NUMZ004, NUMP020, NUMP019, NMUE033
Is pre-requisite for: NALG019, NALG013, NALG012, NALG007, NALG071, NALG072, NALG067, NALG070, NALG078
Is interchangeable with: NMUE033, NUMP007, NUMP019, NMUE004, NUMP020, NUMZ004
Opinion survey results   Examination dates   Schedule   Noticeboard   
Annotation -
Basic concepts and results of commutative algebra. Introduction to Boolean algebras.
Last update: G_M (02.06.2011)
Literature -

S.Lang, Algebra, Revised 3rd ed., GTM 211, Springer, New York, 2002.

N. Lauritzen, Concrete Abstract Algebra, Cambridge Univ. Press, Cambridge 2003.

C. Menini and F. van Oystaeyen: ``Abstract Algebra'', M. Dekker, New York 2004.

L.Procházka a kol., Algebra, Academia, Praha, 1990 (in Czech).

J.Trlifaj, Algebra II, http://www.karlin.mff.cuni.cz/~trlifaj/NALG027.pdf (in Czech).

Last update: T_KA (19.05.2010)
Syllabus -

1. Polynomial rings.

1.1 Divisibility for integral domains. Hilbert Basis Theorem .

1.2 UFD's and Euclidean domains, The Euclid algorithm.

1.3 Derivation and multiplicity of roots, perfect fields.

1.4 Symmetric polynomials, the Main Theorem, and its applications.

2. Fields.

2.1 Field extensions of finite degree.

2.2 Splitting fields, their existence and uniqueness, algebraic closure.

2.3 The structure of finite fields.

3. Lattices and Boolean algebras.

3.1 Complete and modular lattices.

3.2 Boolean algebras, structure of finite Boolean algebras.

Suplementary topic: Introduction to universal algebra. Terms and free algebras.

Last update: T_KA (20.05.2010)