Subjects

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Algebra 2 - NMAG202

Title:	Algebra 2
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2016
Semester:	summer
E-Credits:	4
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Jan Šťovíček, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinné M Bc. MMIB > 2. ročník M Bc. MMIT M Bc. MMIT > Povinné M Bc. OM M Bc. OM > Povinné M Bc. OM > 2. ročník
Classification:	Mathematics > Algebra
Pre-requisite :	{One course in Linear Algebra}
Co-requisite :	NMAG201
Incompatibility :	NALG027
Interchangeability :	NALG027
Is interchangeable with:	NALG027

Annotation -

Last update: T_KA (17.05.2012)

Introductory course for the second year students of mathematics. Commutative algebra and field theory.

Literature -

Last update: doc. RNDr. David Stanovský, Ph.D. (25.09.2017)

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).

D.Stanovský, Základy algebry, Matfyzpress, Praha 2010 (in Czech).

J.Trlifaj: Algebra I, http://www.karlin.mff.cuni.cz/~trlifaj/NALG026.pdf (in Czech).

Syllabus -

Last update: doc. RNDr. David Stanovský, Ph.D. (25.09.2017)

III. Algebraic constructions

Algebra, subalgebra, direct product.

Homomorphism, isomorphic algebras.¨

Quotient groups, quotient rings.

Maximal ideal and prime ideals, constructing fields.

IV. Feilds

Finite extensions.

Splitting fields.

Algebraic numbers, algebraic closure.

Galois group and Galois correspondence.