Commutative algebra

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Introductory course of commutative algebra. Some important applications, such as Gröbner bases and modern methods of factorization are noted.

Requirements:

Syllabus of lectures:

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.

Syllabus of tutorials:

Study Objective:

Knowledge:

Understanding of commutative algebra basics, relations between ideals and varietes, usage of Gröbner bases and factorization of polynomials.

Skills:

various methods of Gröbner bases calculations, factorization methods, working with finite fields.

Study materials:

Key references:

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

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

Recommended references:

3. 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: