Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Commutative Algebra 1 - NMAG460

Title:	Komutativní algebra 1
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Tomáš Kepka, DrSc.
Class:	M Mgr. MSTR
Classification:	Mathematics > Algebra
Is co-requisite for:	NMAG561
Is interchangeable with:	NALG015

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KA (14.05.2013)

Integral extensions, valuation domains, noetherian rings (Artin-Rees theorem), Dedekind domains, integral closures of noetherian domains (separable case, Krull-Akizuki theorem). The knowledge of the material of the course Algebra II (NALG027) is desirable.

Course completion requirements -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)

Students have to pass final test.

Literature - Czech

Last update: T_KA (14.05.2013)

L. Bican, T. Kepka, Komutativní algebra I. (skriptum)

L. Bican, T. Kepka, Komutativní algebra II. (skriptum)

L. Procházka a kol., Algebra

N. Bourbaki, Algébre commutative

Requirements to the exam -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)

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

Syllabus -

Last update: T_KA (14.05.2013)

1. Basic notions (maximal ideals, prime ideals, prime radical, fractional ideals, divisors).

2. Integral extensions (closures, quotient rings and polynomials, extension of homomorphisms).

3. Valoation domains (basic properties, integral closure, basic constructions, power series, domains finitely generated over fields).

4. Noetherian rings (basic properties, Artin-Rees Theorem, primary decomposition).

5. Dedekind domains (invertible ideals, Dedekind domains, Dedekind rings).

6. Integral closures of noetherian domains (separable case, Krull-Akudzuki Theorem).