Theorems · Theorem · commutative algebra
ValuationSubring.coe_mem_principalUnitGroup_iff
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) {x : ↥A.unitGroup},
↑x ∈ A.principalUnitGroup ↔ A.unitGroupMulEquiv x ∈ (Units.map ↑(IsLocalRing.residue ↥A)).ker- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
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- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientproof · cited by 2,301
- Units.valproof · cited by 1,966
- MulEquivstatement · cited by 1,142
- Ideal.Quotient.mkproof · cited by 610
- sub_eq_zeroproof · cited by 407
- IsLocalRing.maximalIdealproof · cited by 297
- MonoidHom.kerstatement · cited by 212
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