List of commutative algebra topics
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This is a list of commutative algebra topics, by Wikipedia page.
- commutative ring
- ring ideal, maximal ideal, prime ideal
- ring monomorphism, ring epimorphism, ring isomorphism
- integral domain
- quotient field
- product of rings
- Boolean algebra
- zero divisor
- nilpotent, reduced (ring theory)
- annihilator
- principal ideal domain
- unique factorization domain
- Dedekind domain
- Fractional ideal
- Ideal class group
- Euclidean domain
- integral closure
- Chinese remainder theorem
- radical of an ideal
- Noetherian ring
- Hilbert's basis theorem
- Hilbert's Nullstellensatz
- Krull dimension
- Lasker-Noether theorem
- formal power series
- local ring
- localization of a ring
- localization of a module
- flat module
- flat map
- projective module
- injective module
- regular local ring
- regular sequence (algebra)
- Cohen-Macaulay ring
- Gorenstein ring
- complete intersection ring
- Zariski tangent space
- Kähler differential
- Dual numbers
- Height (ring theory)
- Krull's principal ideal theorem
- Weierstrass preparation theorem
- Quillen-Suslin theorem
- Koszul complex
- tensor product of fields
- tensor product of R-algebras
- Valuation (mathematics)
- I-adic topology
- Spectrum of a ring.