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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (29.04.2021)
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (29.04.2021)
M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969.
H. Matsumura, Commutative ring theory. Translated from the Japanese by M. Reid. Second edition. Cambridge Studies in Advanced Mathematics, 8. Cambridge University Press, Cambridge, 1989.
W. Bruns, J. Herzog, Cohen-Macaulay rings. Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1993.
D. Eisenbud, Commutative algebra. With a view toward algebraic geometry. Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995. |
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (29.04.2021)
1. Noetherian and Artinian rings. 2. Prime and maximal ideals, the Jacobson radical and the nilradical, Nakayama's lemma. 3. Localization, flatness, integral extensions, going up and going down theorems. 4. Adic completion, the Artin-Rees lemma and the Krull's intersection theorem. 5. Dimension theory of rings and Krull's principal ideal theorem. 6. Regular sequences and Koszul complexes. 7. Basics on Regular, Gorenstein and Cohen-Macaulay rings. 8. Serre theorem about localization of regular rings. |
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (08.11.2021)
Basics of homological algebra (to the extent of lecture NMAG434). |