A set with two operations: (R, +) is an abelian group, · is associative with identity, and · distributes over +. Examples: ℤ, polynomial rings k[x], matrix rings M_n(k).
Ring (R, +, ·)
Related concepts
- Ideal
- Field
- Polynomial ring k[x]
- Integers (ℤ)
- UFD / PID / Euclidean domain hierarchy
- Noetherian ring
- Module over a ring
- Hilbert basis theorem
- Spec(A) as affine scheme
- Nakayama's lemma
- Krull dimension
- Artinian vs Noetherian
- Dedekind domain
- UFD ⊃ PID ⊃ Euclidean domain
- Lie algebra
- Chain complex
- Global dimension of a ring
- Baer's criterion for injectivity
- Koszul complex