Theorems · Inductive type · commutative algebra
SubsemiringClass
(S : Type u_1) → (R : outParam (Type u)) → [NonAssocSemiring R] → [SetLike S R] → Prop
SubsemiringClass S R states that S is a type of subsets s ⊆ R that
are both a multiplicative and an additive submonoid.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Defs
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- NonAssocSemiringSetLike
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.
- SetLikestatement · cited by 1,084
- NonAssocSemiringstatement · cited by 805
Cited by44
Results whose statement or proof uses this declaration.
- RingHom.codRestrictstatement and proof · cited by 12
- SubsemiringClass.subtypestatement and proof · cited by 5
- RingHom.domRestrictstatement and proof · cited by 5
- SubalgebraClass.valstatement and proof · cited by 3
- RingEquiv.restrictstatement and proof · cited by 3
- RingHom.restrictstatement and proof · cited by 3
- RingHom.injective_codRestrictstatement and proof · cited by 3
- StarSubalgebra.ofClassstatement and proof · cited by 2
- Subsemiring.ofClassstatement and proof · cited by 2
- StarSubalgebra.ofClass_carrierstatement and proof · cited by 1
- Algebra.algebraMap_ofSubsemiring_applystatement and proof · cited by 1
- StarSubsemiring.ofClassstatement and proof · cited by 1