Learn · Commutative Algebra with a Viewpoint towards Algebraic Number Theory
Lecture 26 of 37Week 5 Dedekind Domains
Ring of Integers are Dedekind Domains
Prof. Bharathwaj Palvannan · IISc Bangalore
Credits and licence
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- Commutative Algebra with a Viewpoint towards Algebraic Number Theory, IISc Bangalore (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Integral Element
- Integral Closure
- Integral Closure, Trace and Norm
- Integral closure of a Noetherian integrally closed domain
- Ring of Algebraic Integers
- Going up theorem
- Local rings and localizations
- V and V* rings
- Valuation and Valuation ring
- V-rings are valuation rings
- Maximal local rings inside fields
- Maximal local rings and Valuation rings
- A characterization of integrally closed domains involving valuation rings
- Discrete Valuation rings-1
- Discrete Valuation rings-2
- Classification of Discrete Valuation rings containing ℤ and Fp[t]
- p-adic absolute value
- ℚ is a topological field
- p-adic numbers
- p-adic integers
- p-adic integers as a completion
- p-adic expansion of p-adic integers
- Hensel's lemma
- Dedekind Domains
- Unique Factorisation of Ideals in Dedekind Domains
- Ring of Integers are Dedekind Domains
- Galois extensions
- Decomposition Groups
- Ramification indices and residue field degrees
- efg theorem
- Inertia group
- Class Groups
- Equivalent characterisation of invertible fractional ideals
- Basic PID
- Norm Estimates
- Finiteness of Class group I
- Finiteness of Class group II