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Course, academic year 2023/2024
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Commutative Algebra 1 - NALG015
Title: Komutativní algebra 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1, C+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
Teaching methods: full-time
Guarantor: prof. RNDr. Tomáš Kepka, DrSc.
Classification: Mathematics > Algebra
Interchangeability : NMAG460
Is co-requisite for: NALG074
Annotation -
Last update: G_M (02.06.2011)
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.
Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

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

Syllabus -
Last update: T_KA (16.05.2005)

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).

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