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Commutative Rings - NMAG301

Title:	Komutativní okruhy
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:3/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://www2.karlin.mff.cuni.cz/~stanovsk/vyuka/komutalg.htm

Guarantor:	doc. RNDr. David Stanovský, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinné M Bc. MMIT M Bc. MMIT > Povinné M Bc. OM M Bc. OM > Zaměření MSTR M Bc. OM > Povinně volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NMAG305
Interchangeability :	NMAG305
Is incompatible with:	NMAG305
Is interchangeable with:	NMAG305
In complex pre-requisite:	NMAG349

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: G_M (15.05.2012)

A recommended course for Information Security and specialization Mathematical Structures within General Mathematics. It covers basic topics of commutative ring theory.

Course completion requirements -

Last update: doc. RNDr. David Stanovský, Ph.D. (28.09.2020)

Students have to solve 3 series of homeworks.

Literature -

Last update: doc. RNDr. David Stanovský, Ph.D. (28.09.2020)

Fundamental sources:

Other books:

M. F. Atiah, I.G. Macdonald, Introduction to Commutative Algebra, Addison Wesley, 1969.
H. Matsumura, Commutative Ring Theory, W. A. Benjamin, 1970.
P. Samuel, O. Zariski, Commutative Algebra vol. I and II, Princeton, D. Van Nostrand Company, 1958, 1960.
R. Y. Sharp, Steps in Commutative Algebra (London Math. Society Student Text), Cambridge Univ. Press, 2nd ed., 2001.

Requirements to the exam -

Last update: doc. RNDr. David Stanovský, Ph.D. (28.09.2020)

Students have to pass final exam. The requirements for the exam correspond to what has been done during lectures and practicals.

Syllabus -

Last update: doc. RNDr. David Stanovský, Ph.D. (28.09.2020)

Fundamentals - ideals, radical, notherian property, chinese remainder theorem

Galois theory - splitting fields, algebraic closure, Galois correspondence

Introduction to algebraic geometry - the IV correspondence, Hilbert's Nullstellensatz, irreducible decomposition

Introduction to algebraic number theory - integral extensions, Dedekind domains