Theorems · Definition · commutative algebra
SubsemiringClass.subtype
{R : Type u} →
{S : Type v} →
[inst : NonAssocSemiring R] → [inst_1 : SetLike S R] → [hSR : SubsemiringClass S R] → (s : S) → ↥s →+* RThe natural ring hom from a subsemiring of semiring R to R.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- MonoidHomproof · cited by 3,629
- AddMonoidHomproof · cited by 3,230
- SetLikestatement and proof · cited by 1,084
- NonAssocSemiringstatement and proof · cited by 805
- SubsemiringClassstatement and proof · cited by 30
- AddSubmonoidClass.subtypeproof · cited by 12
- SubmonoidClass.subtypeproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- RingHom.domRestrictproof · cited by 5
- SubalgebraClass.valproof · cited by 3
- CentroidHom.centerToCentroidproof · cited by 2
- RingHom.rangeS_codRestrictstatement and proof · cited by 0
- RingHom.comp_restrictstatement · cited by 0
- CentroidHom.centerStarEmbeddingproof · cited by 0
- SubsemiringClass.coe_subtypestatement · cited by 0
- SubsemiringClass.subtype_applystatement · cited by 0
- SubsemiringClass.subtype_injectivestatement · cited by 0