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250031 VO Computational Commutative Algebra (2020W)
Labels
Registration/Deregistration
Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Tuesday 06.10. 14:00 - 14:45 Digital
- Wednesday 07.10. 14:00 - 15:30 Digital
- Tuesday 13.10. 14:00 - 14:45 Digital
- Wednesday 14.10. 14:00 - 15:30 Digital
- Tuesday 20.10. 14:00 - 14:45 Digital
- Wednesday 21.10. 14:00 - 15:30 Digital
- Tuesday 27.10. 14:00 - 14:45 Digital
- Wednesday 28.10. 14:00 - 15:30 Digital
- Tuesday 03.11. 14:00 - 14:45 Digital
- Wednesday 04.11. 14:00 - 15:30 Digital
- Tuesday 10.11. 14:00 - 14:45 Digital
- Wednesday 11.11. 14:00 - 15:30 Digital
- Tuesday 17.11. 14:00 - 14:45 Digital
- Wednesday 18.11. 14:00 - 15:30 Digital
- Tuesday 24.11. 14:00 - 14:45 Digital
- Wednesday 25.11. 14:00 - 15:30 Digital
- Tuesday 01.12. 14:00 - 14:45 Digital
- Wednesday 02.12. 14:00 - 15:30 Digital
- Wednesday 09.12. 14:00 - 15:30 Digital
- Tuesday 15.12. 14:00 - 14:45 Digital
- Wednesday 16.12. 14:00 - 15:30 Digital
- Tuesday 12.01. 14:00 - 14:45 Digital
- Wednesday 13.01. 14:00 - 15:30 Digital
- Tuesday 19.01. 14:00 - 14:45 Digital
- Wednesday 20.01. 14:00 - 15:30 Digital
- Tuesday 26.01. 14:00 - 14:45 Digital
- Wednesday 27.01. 14:00 - 15:30 Digital
Information
Aims, contents and method of the course
The aim of this lecture is to study commutative rings, their ideals and modules over commutative rings. This can serve as a basis for algebraic geometry, invariant theory, algebraic number theory and other subjects. We will cover the basic notions, and introduce, among other things, localizations, Noetherian rings, affine algebraic sets, Groebner bases, modules, integral extensions, Dedekind rings and discrete valuation rings. Moreover we will consider the computational aspects of the theory and compute several examples. Here the computation of Groebner bases and its applications is one of the main goals.
Assessment and permitted materials
There will be a written examination after the end of the lecture. There are no tools allowed.
Minimum requirements and assessment criteria
50 percent of the total points required to pass.
Examination topics
Exam material contains all topics covered in the lecture including examples and computations.
Reading list
[AM] M.F. Atiyah, I.G. Macdonald: Introduction to commutative Algebra, 1969.
[COX] D. Cox, J. L. Donal O’Shea: Geometry, Algebra, and Algorithms.
[EIS] D. Eisenbud, Commutative Algebra, 1995.
[SAZ] P. Samuel, O. Zariski: Commutative Algebra, 1975.
[SHA] R. Y. Sharp: Steps in commutative algebra, 2000.
[COX] D. Cox, J. L. Donal O’Shea: Geometry, Algebra, and Algorithms.
[EIS] D. Eisenbud, Commutative Algebra, 1995.
[SAZ] P. Samuel, O. Zariski: Commutative Algebra, 1975.
[SHA] R. Y. Sharp: Steps in commutative algebra, 2000.
Association in the course directory
MALV, MAMV
Last modified: Fr 12.05.2023 00:21