Commutative Algebra

Garant předmětu:

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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.

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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:

Further information:

No time-table has been prepared for this course

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)