SYLLABUS
Mathematics 6150
Commutative Algebra
This is a rough guide to the topics we will cover.
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Week 1
|
Review
|
Week 2
|
Rings and ideals
|
Week 3
|
Modules
|
Week 4
|
Rings and modules of fractions
|
Week 5
|
Primary decomposition
|
| Week 6 |
Integral dependence and
valuations
|
Week 7
|
Chain conditions
|
| Week 8 |
Noetherian rings
|
| Week 9 |
Artin Rings
|
| Week 10 |
Discrete valuation rings and
Dedekind domains
|
| Week 11 |
Completions
|
| Week 12 |
Dimension theory
|
| Week 13 |
Derivations and differentials
|
| Week 14 |
Further topics
|
Week 15
|
Review
|