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MU:MU25015 Chapters in Algebra - Course Information

## MU25015 Chapters in Algebra

**Mathematical Institute in Opava**

Summer 2021

The course is not taught in Summer 2021

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- doc. RNDr. Michal Marvan, CSc. (lecturer)

RNDr. Hynek Baran, Ph.D. (seminar tutor) **Guaranteed by**- doc. RNDr. Michal Marvan, CSc.

Mathematical Institute in Opava **Prerequisites**(in Czech)- TYP_STUDIA ( N )
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Geometry and Global Analysis (programme MU, NMgr-M)
- Mathematical Analysis (programme MU, NMgr-M)
- Mathematical Modelling (programme MU, NMgr-M)

**Course objectives**- Chapters in algebra cover advanced algebraic topics, appropriate for all graduates of mathematics.
**Syllabus**- 1. Integral domains, divisibility, Euclidean domains, principal ideal domains, unique factorization domains, field of fractions over an integral domain, resultant and discriminant.

2. Algebraic and transcendental extensions, algebraic number fields.

3. Systems of polynomial equations and their solutions, polynomial ideals, Hilbert's basis theorem.

4. Groebner bases, Buchberger algorithm, arithmetics in quotient rings of polynomial rings.

5. Algebraic varieties, radical ideals, sums, products and intersections of algebraic varieties, irreducible varieties and prime ideals.

6. Groups, algebras and their representations, group modules, irreducible representations.

- 1. Integral domains, divisibility, Euclidean domains, principal ideal domains, unique factorization domains, field of fractions over an integral domain, resultant and discriminant.
**Literature****Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- The course comprises lectures and tutorials. To pass the course, the first step is to earn credit for tutorials (by earning 70% on a written test). The final exam, which consists of a written and on oral part, tests theoretical knowledge and understanding of the subject, including proofs.

- Permalink: https://is.slu.cz/course/sumu/summer2021/MU25015