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Instructor: Chitrabhanu Chaudhuri (office M-227, email: chitrabhanu [at] niser [dot] ac [dot] in) |
Texts:
- M. F. Atiyah, I. G. Macdonald, “Introduction to Commutative Algebra”, AddisonWesley Publishing Co., 1969.
- R. Y. Sharp, “Steps in Commutative Algebra”, London Mathematical Society Student Texts, 51. Cambridge University Press, 2000.
- D. S. Dummit, R. M. Foote, “Abstract Algebra”, Wiley-India edition, 2013.
References:
- David Eisenbud, “Commutative Algebra with a view toward Algebraic Geometry”, Springer, 3rd Edition 1999.
- James S. Milne, A Primer of Commutative Algebra.
- Hideyuki Matsumura, "Commutative Ring Theory", Cambridge Studies in Advanced Mathematics, Cambridge University Press, 1989.
- Miles Reid, "Undergraduate Commutative Algebra", London Mathematical Society student texts 29, Cambridge University Press, 1995.
Course Resources folder will contain lecture notes and problem sets. Please book mark this folder.
Problem Sets: There will be weekly problem sets and every Monday there will be a problem session based on the previous week's problem set.
Exams: Test1 19 Sep (Mon); Test2 7 Nov (Mon); Midsem 30 September(Friday) 14:30-16:30; Endsem 12 Dec (Monday) 10:00-13:00.
Grading percentages: Test1 - 15%, Test2 - 15%, Midterm - 30%, Final - 40%.
Topics Covered:
- Week 1 (8-12 Aug): Commutative Rings, Prime ideals, Maximal ideals, Extension and Contraction of ideals.
- Week 2 (15-19 Aug): Nilradical, Jacobson Radical, Local Rings, Spectrum of a Ring.
- Week 3 (22-26 Aug): Modules, Cayley Hamilton theorem, Nakayama's Lemma.
- Week 4 (29 Aug-2 Sep): Exact Sequences of Modules, Snake Lemma, Projective and Injective Modules.
- Week 5 (5-9 Sep): Tensor product of Modules and Algebras, Extension and Restriction of scalars, Flat modules.
- Week 6 (12-16 Sep): Localisation of Rings and Modules, Local properties, Extension of ideals under localisation.
- Week 7 (19-23 Sep): Integral Extensions, Normal domains, Going up and Going down theorems.
- Week 8 (10-14 Oct): Noether normalisation, Hilbert Nullstellensatz and applications.
- Week 9 (17-21 Oct): Noetherian Rings and Modules.
- Week 10 (24-28 Oct): Primary Decomposition Theorem.
- Week 11 (31 Oct-4 Nov): Artinian Rings.
- Week 12 (7-11 Nov): Discrete Valuation Rings and Dedekind domains.
- Week 13 (14-18 Nov): Dedekind domains and Fractional ideals.
- Week 14 (21-25 Nov):