Theorems · Theorem · commutative algebra
ValuationSubring.coe_unitGroupToResidueFieldUnits_apply
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (x : ↥A.unitGroup),
↑(A.unitGroupToResidueFieldUnits x) = (Ideal.Quotient.mk (IsLocalRing.maximalIdeal ↥A)) ↑(A.unitGroupMulEquiv x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Idealstatement · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement · cited by 2,301
- Units.valstatement · cited by 1,966
- MulEquivstatement · cited by 1,142
- Ideal.Quotient.mkstatement · cited by 610
- IsLocalRing.maximalIdealstatement · cited by 297
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