Theorems · Definition · commutative algebra
Subring.subtype
{R : Type u} → [inst : NonAssocRing R] → (s : Subring R) → ↥s →+* RThe natural ring hom from a subring of ring R to R.
- Defined in
- Mathlib.Algebra.Ring.Subring.Defs
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subsemiring.toSubmonoidproof · cited by 153
- AddSubgroup.subtypeproof · cited by 82
- Subring.toSubsemiringproof · cited by 71
- Submonoid.subtypeproof · cited by 26
- Subring.toAddSubgroupproof · cited by 11
Cited by32
Results whose statement or proof uses this declaration.
- Subring.inclusionproof · cited by 13
- Polynomial.map_toSubringstatement and proof · cited by 6
- RingEquiv.ofLeftInverseproof · cited by 5
- FixedPoints.minpoly.eval₂statement and proof · cited by 5
- RingHom.pullbackFstproof · cited by 4
- CommRingCat.equalizerForkproof · cited by 3
- IsInvariantSubring.subtypeHomproof · cited by 3
- RingHom.pullbackSndproof · cited by 3
- ValuationSubring.subtypeproof · cited by 3
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- Subring.subtype_injectivestatement · cited by 2
- Subalgebra.toSubring_subtypestatement · cited by 2