Math 2.0

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Commutative Algebra with a Viewpoint towards Algebraic Number Theory GBA32PSBH2

URIm2://res/GBA32PSBH2
Kindcourse
CreatorsBharathwaj Palvannan (instructor)
Date2026-06-18
Scopein
Idscourse 04dese585:111108003

Expressions

e1: edition

Languageen
Date2026-06-18
Contents
  • part 1: Week 1 Integral extensions
  • session 1: Integral Element
  • session 2: Integral Closure
  • session 3: Integral Closure, Trace and Norm
  • session 4: Integral closure of a Noetherian integrally closed domain
  • session 5: Ring of Algebraic Integers
  • session 6: Going up theorem
  • part 2: Week 2 Valuation rings
  • session 7: Local rings and localizations
  • session 8: V and V* rings
  • session 9: Valuation and Valuation ring
  • session 10: V-rings are valuation rings
  • session 11: Maximal local rings inside fields
  • session 12: Maximal local rings and Valuation rings
  • session 13: A characterization of integrally closed domains involving valuation rings
  • part 3: Week 3 Discrete Valuation Rings
  • session 14: Discrete Valuation rings-1
  • session 15: Discrete Valuation rings-2
  • session 16: Classification of Discrete Valuation rings containing ℤ and Fp[t]
  • part 4: Week 4 Completions and Hensel's lemma
  • session 17: p-adic absolute value
  • session 18: ℚ is a topological field
  • session 19: p-adic numbers
  • session 20: p-adic integers
  • session 21: p-adic integers as a completion
  • session 22: p-adic expansion of p-adic integers
  • session 23: Hensel's lemma
  • part 5: Week 5 Dedekind Domains
  • session 24: Dedekind Domains
  • session 25: Unique Factorisation of Ideals in Dedekind Domains
  • session 26: Ring of Integers are Dedekind Domains
  • part 6: Week 6 Galois extensions of global fields
  • session 27: Galois extensions
  • session 28: Decomposition Groups
  • session 29: Ramification indices and residue field degrees
  • session 30: efg theorem
  • session 31: Inertia group
  • part 7: Week 7 Class groups
  • session 32: Class Groups
  • session 33: Equivalent characterisation of invertible fractional ideals
  • part 8: Week 8 Finiteness of Class group
  • session 34: Basic PID
  • session 35: Norm Estimates
  • session 36: Finiteness of Class group I
  • session 37: Finiteness of Class group II

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