Commutative Algebra

Course guarantor:

Severin Pošta

Lecturer:

Severin Pošta

Tutor:

Severin Pošta

Supervisor:

Department of Mathematics

Synopsis:

1. Rings, ideals, homomorphisms, prime and maximal ideals.

2. Rings of polynomials, symmetric polynomials, irreducibility.

3. Gröbner bases.

4. Polynomials with rational coefficients, factorization of polynomials.

5. Hilbert's Nullstellensatz, ideals and manifolds, Krull dimension.

6. Fields, extensions, finite fields.

7. Introduction to Galois theory, Galois extensions, group and correspondence.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Povinná literatura

1. G. Kemper: A course in commutative algebra, Springer, 2010.

2. R. Y Sharp: Steps in commutative algebra, Cambridge, 2000.

3. D. Stanovský, L. Barto: Počítačová algebra, Matfyzpress, 2017.

Doporučená literatura

4. D. Stanovský: Základy algebry, Matfyzpress 2010.

5. L. Procházka, L. Bican, T. Kepka, P. Němec: Algebra, Academia, 1990.

6. D. Eisenbud: Commutative Algebra: with a View Toward Algebraic Geometry, Springer, 2013.

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomTR:112 Pošta S. 08:00–09:50 (lecture parallel1) Trojanova 13
Tue
Wed
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (compulsory course in the program)
• Matematická informatika (compulsory course in the program)