Categories of Modules and Homological Algebra - NALG029
Title: Kategorie modulů a homologická algebra
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Trlifaj, CSc., DSc.
Classification: Mathematics > Algebra
Interchangeability : NMAG434
Is incompatible with: NMAG434
Is interchangeable with: NMAG434
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Annotation -
Category theory of modules (covariant and contravariant Hom functors, projective and injective modules, tensor product, flat modules, adjointness of Hom functors and tensor product, Morita equivalence of rings and its characterization, a generalization: tilting modules and tilted algebras), introduction to homological algebra (complexes, projective and injective resolutions, Extn and Torn functors, connections between Ext1 and extensions of modules.
Last update: G_M (05.10.2001)
Literature - Czech

F.W.Anderson, K.R.Fuller: Rings and Categories of Modules, Springer, New York 1992.

J. J. Rotman, An Introduction to Homological Algebra, Academic Press, San Diego, 1979.

C.Weibel: An Introduction to Homological Algebra, Cambridge Univ.Press, Cambridge, 1994.

Last update: T_KA (08.04.2008)
Syllabus -

Category theory of modules (covariant and contravariant Hom functors, projective and injective modules, tensor product, flat modules, adjointness of Hom functors and tensor product, Morita equivalence of rings and its characterization, a generalization: tilting modules and tilted algebras), introduction to homological algebra (complexes, projective and injective resolutions, Extn and Torn functors, connections between Ext1 and extensions of modules.

Last update: T_KA (10.05.2004)
Entry requirements -

Basics of ring and module theory.

Last update: T_KA (11.04.2008)