Theorems · Definition · commutative algebra
ValuationSubring.inclusion
{K : Type u} → [inst : Field K] → (R S : ValuationSubring K) → R ≤ S → ↥R →+* ↥SThe ring homomorphism induced by the partial order.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- ValuationSubringstatement and proof · cited by 187
- Subring.inclusionproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- ValuationSubring.idealOfLEproof · cited by 7
- ValuationSubring.monotone_mapOfLEproof · cited by 3
- ValuationSubring.ofPrime_idealOfLEproof · cited by 2
- ValuationSubring.idealOfLE_le_of_leproof · cited by 0
- ValuationSubring.idealOfLE_topproof · cited by 0
- ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdealstatement · cited by 0
- ValuationSubring.inclusion.congr_simpstatement and proof · cited by 0