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| This is a graduate course in commutative algebra. The course will cover primary decomposition, integral dependence, discrete valuation rings, completions and dimension theory. If time permits we will add some additional topics, based on participants interests. Prerequisites are some knowledge in abstract algebra, as for instance SF2737 Commutative Algebra and Algebraic Geometry. | |||
| The course book will be "Introduction to Commutative Algebra" by Atiyah and MacDonald. The participants are assumed to be familiar with the contents of the three first chapters. | |||
| The participants will have to take an active role in the course by preparing selected lectures and by constructing examples. In addition there will be a number of home assignments. These activities are also the basis for the examination, where only grades P/F (pass/fail) are given. |
| Tentative plan | |||
| Sept 7, Monday 15.15-17.00 |
KTH 3418 |
Roy: Repetition, Chapters 1-2. |
Exercises Done (21.09) |
| Mo 14.09 15.15-17.00 |
KTH 3418 |
Roy: Chapter 3-4. |
Exercises Done (28.09) |
| Mo 21.09 15.15-17.00 |
KTH 3418 |
Roy: Chapter 4. Nasrin: Going-up, pp 59-62. |
Exercises (Done 05.10) |
| Mo 28.09 15.15-17.00 |
KTH 3418 |
Roy: Exercise session |
Exercises (Done 12.10) |
| Oct 5, Monday 15.15-17.00 |
KTH 3418 |
Sven: Going-down, pp 62-64 George: Chain conditions, pp 74-78. |
Exercises |
| Mo 12.10 15.15-17.00 |
KTH 3418 |
Exercise session Nasrin: Noetherian rings, pp 80-84. |
Exercises (Done 19.10) |
| Mo 19.10 15.15-17.00 |
KTH 3418 |
Exercise session George: Artin rings, pp 89-91. |
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| Mo 26.10 15.15-17.00 |
KTH xxxx |
No lecture. |
Homework 1 (remark added 20.10) Deadline 26.10, at 24.00. |
| Nov 2, Monday 15.15-17.00 |
KTH 3418 |
Exercise session Roy: Completions, Ch 10 |
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| Mo 09.11 15.15-17.00 |
KTH 3652 |
Roy: Filtrations, Ch 10 | Exercises (Done 16.11) |
| Mo 16.11 15.15-17.00 |
KTH 3652 |
Exercise session Roy: Associated Graded ring, Ch 10 |
Exercises (Done 23.11) |
| Mo 23.11 15.15-17.00 |
KTH 3652 |
Exercise session Roy: Dimension theory, Ch 11 |
Exercises (Done 30.10) |
| Mo 30.11 15.15-17.00 |
KTH 3652 |
Exercises Roy: Dimension theory, Ch 11 |
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| Dec 7, Monday 15.15-17.00 |
KTH 3652 |
No lecture |
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| Mo 14.12 15.15-17.00 |
KTH 3652 |
No lecture |
Homework 2. Deadline 21.12, at 24:00. |
| The page is maintained by Roy Skjelnes. |