Commutative Algebra

Start reading → Chapter VIII

1. VIIIDimension
   1. Chapter VIII
   2. § 1. Krull dimension of a ring48
   3. § 2. Dimension of algebras32
   4. § 3. Dimension of noetherian rings37
   5. § 4. Hilbert-samuel series34
   6. § 5. Regular local rings31
   7. § 6. Dimension of graded rings27
   8. § 7. Multiplicities28
2. IXComplete noetherian local rings
   1. Chapter IX
   2. § 1. Witt vectors29
   3. § 2. Cohen rings30
   4. § 3. Fields of representatives7
   5. § 4. Integral closure of a complete local ring25
   6. App. 0. Exercises13
3. XDepth, regularity, duality
   1. Chapter X
   2. § 1. Depth60
   3. § 2. Macaulay modules and rings46
   4. § 3. Depth and homological dimension43
   5. § 4. Regular rings29
   6. § 5. Complete intersections20
   7. § 6. Extension of scalars in regular algebras33
   8. § 7. Smooth algebras39
   9. § 8. Duality of modules of finite length31
   10. § 9. Dualizing modules31
   11. § 10. Local cohomology, grothendieck duality20