Theorems · Inductive type · ring theory
Algebra
(R : Type u) → (A : Type v) → [CommSemiring R] → [Semiring A] → Type (max u v)
An associative unital R-algebra is a semiring A equipped with a map into its center R → A.
See the implementation notes in this file for discussion of the details of this definition.
- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 11,388 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- CommSemiringSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- CommSemiringstatement · cited by 10,911
Cited by13,826
Results whose statement or proof uses this declaration.
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement · cited by 3,236
- AlgEquivstatement · cited by 1,681
- Subalgebrastatement · cited by 1,353
- IntermediateFieldstatement · cited by 988
- IsFractionRingstatement and proof · cited by 738
- IsLocalizationstatement · cited by 636
- AlgEquiv.symmstatement and proof · cited by 615
- Polynomial.aevalstatement and proof · cited by 615
- Algebra.adjoinstatement and proof · cited by 535
- spectrumstatement and proof · cited by 510
- AlgHom.compstatement and proof · cited by 501
Showing the 200 most cited of 13,826.