## M5110 Rings and Modules

Faculty of Science
Autumn 2003
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable of Seminar Groups
M5110/01: No timetable has been entered into IS. J. Rosický
Prerequisites
M2150 Algebra I && M2110 Linear Algebra 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 presents one of fundamental topics of modern algebra. It naturally follows the well-known theory of vector spaces and shows what happens if scalars form a ring and not a field. It presents the emerging concepts of projective, flat and injective modules and their structure properties. Doing it, there are used basic constructions like products, direct sums, kernels, cokernels and tensor products. The course prepares students to the use of modules in geometry and topology.
Syllabus
• 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 sequaences: short exact sequences, group Ext 6. Injective modules: injective modules, injective hull
Literature
• L.Rowen, Ring theory I, Academic Press 1988
• A.J.Berrick, M.E.Keating, An introduction to rings and modules, Cambridge Univ. Press 2000
Assessment methods (in Czech)
Výuka: přednáška Zkouška: ústní
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017.
• Enrolment Statistics (Autumn 2003, recent)