Theorems · Definition · commutative algebra
ValuationSubring.ofLE
{K : Type u} → [inst : Field K] → (R : ValuationSubring K) → (S : Subring K) → R.toSubring ≤ S → ValuationSubring KAn overring of a valuation ring is a valuation ring.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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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.
- Fieldstatement and proof · cited by 7,404
- Subringstatement and proof · cited by 602
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.toSubringstatement and proof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- ValuationSubring.ofPrimeproof · cited by 10