List of commutative algebra topics
From Wikipedia, the free encyclopedia
This is a list of commutative algebra topics, by Wikipedia page.
[edit] Research fields
[edit] Basic notions
- commutative ring
- module (mathematics)
- ring ideal, maximal ideal, prime ideal
- ring homomorphism
- zero divisor
- Chinese remainder theorem
[edit] Classes of rings
- field (mathematics)
- algebraic number field
- polynomial ring
- integral domain
- Boolean algebra (structure)
- principal ideal domain
- Euclidean domain
- unique factorization domain
- Dedekind domain
- nilpotent, reduced ring
- dual numbers
- tensor product of fields
- tensor product of R-algebras
[edit] Constructions with commutative rings
[edit] Localization and completion
- completion (ring theory)
- formal power series
- local ring
- regular local ring
- localization of a ring
- localization of a module
- valuation (mathematics)
- I-adic topology
- Weierstrass preparation theorem
[edit] Finiteness properties
- Noetherian ring
- Hilbert's basis theorem
- Artinian ring
- ascending chain condition (acc) and descending chain condition (dcc)
[edit] Ideal theory
[edit] Homological properties
- flat module
- flat map
- projective module
- injective module
- Cohen-Macaulay ring
- Gorenstein ring
- complete intersection ring
- Koszul complex
- Hilbert's syzygy theorem
- Quillen–Suslin theorem
[edit] Dimension theory
- height (ring theory)
- depth (ring theory)
- Hilbert polynomial
- regular local ring
- global dimension
- regular sequence (algebra)
- Krull dimension
- Krull's principal ideal theorem
[edit] Ring extensions, primary decomposition
- primary ideal
- primary decomposition, Lasker–Noether theorem
- Noether normalization lemma
- going up and going down
