Theorems · Definition · commutative algebra
ValuationSubring.unitGroupOrderEmbedding
{K : Type u} → [inst : Field K] → ValuationSubring K ↪o Subgroup KˣThe map on valuation subrings to their unit groups is an order embedding.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 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.
Cites8
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
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- OrderEmbeddingstatement · cited by 619
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.unitGroupproof · cited by 16
- ValuationSubring.unitGroup_injectiveproof · cited by 1
- ValuationSubring.unitGroup_le_unitGroupproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- ValuationSubring.unitGroup_strictMonoproof · cited by 0