Theorems · Definition · commutative algebra
Subring.inclusion
{R : Type u} → [inst : NonAssocRing R] → {S T : Subring R} → S ≤ T → ↥S →+* ↥TThe ring homomorphism associated to an inclusion of subrings.
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRing
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.
- RingHomstatement · cited by 10,189
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subring.subtypeproof · cited by 22
- RingHom.codRestrictproof · cited by 12
Cited by15
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.awayMapproof · cited by 27
- ValuationSubring.inclusionproof · cited by 6
- ValuationSubring.isMax_toLocalSubringproof · cited by 2
- Ideal.image_subset_nonunits_valuationSubringproof · cited by 2
- HomogeneousLocalization.val_awayMap_eq_auxproof · cited by 2
- LocalSubring.exists_le_valuationSubringproof · cited by 2
- IsLocalRing.exists_factor_valuationRingproof · cited by 1
- LocalSubring.map_maximalIdeal_eq_top_of_isMaxstatement and proof · cited by 1
- LocalSubring.mem_of_isMax_of_isIntegralproof · cited by 1
- Subring.inclusion_injectivestatement · cited by 1
- LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedInproof · cited by 1
- bijective_rangeRestrict_comp_of_valuationRingproof · cited by 1