PřF:M5110 Rings and Modules - Course Information
M5110 Rings and ModulesFaculty of Science
- Extent and Intensity
- 2/1. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Mgr. Ivan Di Liberti, Ph.D. (seminar tutor)
- Guaranteed by
- prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
- Mon 18. 9. to Fri 15. 12. Wed 10:00–11:50 M2,01021
- Timetable of Seminar Groups:
- M2110 Linear Algebra II || ( FI:MA004 Linear Algebra and Geometry II )
Algebra: vector spaces, rings
- 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
- Course objectives
- The course introduces students to the theory of modules, one of fundamental topics of modern algebra.
At the end of the course students should be able to:
*explain basic notions (modules, homomorphisms, submodules, quotient modules, products, direct sums, tensor products);
*know the basics of the theory of projective, flat and injective modules and their structure properties;
*understand module theory as an extension of linear algebra and connections to universal algebra;
*apply module theory in geometry and topology.
- Modules: modules, submodules, homomorphisms, quotient modules, products, direct sums, kernels, cokernels 2. Free and projective modules: free modules, projective modules, semisimple rings, vector spaces 3. Tensor product: tensor product and its properties 4. Flat modules: flat modules, directed colimits, Lazard's theorem, regular rings 5. Short exact sequences: short exact sequences, group Ext 6. Injective modules: injective modules, injective hull
- A.J.Berrick, M.E.Keating, An introduction to rings and modules, Cambridge Univ. Press 2000
- L.Rowen, Ring theory I, Academic Press 1988
- Teaching methods
- The course is offered two hours each week plus one hour of exercises. It initiates a discussion with students.
- Assessment methods
- Course ends by an oral exam. Presence at the course is recommended, at the exercises is obligatory. Homeworks are given but not controled.
- Language of instruction
- Further comments (probably available only in Czech)
- Study Materials
The course is taught once in two years.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/autumn2017/M5110