Theorems · Definition · ring theory
Subalgebra.toSubsemiring
{R : Type u} →
{A : Type v} →
[inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → Subalgebra R A → Subsemiring AReinterpret a Subalgebra as a Subsemiring.
- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 115 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 84 definitions · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- Subsemiringstatement · cited by 456
Cited by156
Results whose statement or proof uses this declaration.
- Subalgebra.mapproof · cited by 90
- IntermediateField.restrictScalarsproof · cited by 66
- StarAlgebra.adjoinproof · cited by 42
- IntermediateField.toSubfieldproof · cited by 38
- Subalgebra.restrictScalarsproof · cited by 36
- Subalgebra.toSubringproof · cited by 30
- Subalgebra.opproof · cited by 30
- Subalgebra.topologicalClosureproof · cited by 26
- Subalgebra.comapproof · cited by 23
- Subalgebra.unopproof · cited by 21
- Subalgebra.starClosureproof · cited by 12
- Subalgebra.toNonUnitalSubalgebraproof · cited by 11