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.
Last update: G_M (02.06.2011)
Základy komutativní algebry, celistvá rozšíření, valuační obory,
noetherovské a Dedekindovy okruhy.
Předpokládá se znalost v rozsahu kurzu Algebra II (NALG027).
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).