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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (29.04.2021)
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Last update: Liran Shaul, Ph.D. (17.02.2020)
In order to complete the course, the student must submit all the homework and to get a pass grade in all the homework. |
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Last update: T_KA (09.05.2013)
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. |
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (29.04.2021)
1. Category theory of modules:
1.1 Covariant and contravariant Hom functors, projective and injective modules, 1.2 Tensor product, flat modules, 1.3 Adjointness of Hom functors and tensor product, 1.4 Morita equivalence of rings and its characterization.
2. Introduction to homological algebra:
2.1 Complexes, projective and injective resolutions, 2.2 Ext^n and Tor_n functors, 2.3 Long exact sequences for Ext and Tor, 2.4 Connections between Ext^1 and extensions of modules, 2.5 The homotopy category of complexes and derived categories, 2.6 Triangulated categories. |
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Last update: T_KA (09.05.2013)
Basics of ring and module theory. |