MA036 Rings and modules

Faculty of Informatics
Autumn 2003
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
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.
Prerequisites
! M036 Rings and modules
Algebra: vector spaces, rings
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
There are presented basic concepts of the ring and module theory. An emphasis is on free and injective modules and on the related concepts.
Syllabus
  • Rings and modules: submodules, sums and products, direct and inverse limits.
  • Free and projective modules: semisimple rings, vector spaces. Tensor product.
  • Flat modules: Lazard's characterization.
  • Short exact sequances: the group Ext.
  • Injective modules: injective hulls.
Literature
  • L. Rowen, Ring theory I, Academic Press 1988.
  • A. J. Berrick and M. E. Keating, An introduction to rings and modules, Cambridge Univ. Press 2000.
Assessment methods (in Czech)
výuka: přednáška, cvičení zkouška: písemná nebo ústní
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught: every week.
  • Enrolment Statistics (recent)
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