Theorems · Theorem · commutative algebra

Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange

∀ {F : Type u} {Γ₀ : Type v} [inst : Field F] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation F Γ₀}
  {O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O F],
  v.Integers O → ∀ [Subsingleton (↥(MonoidHom.mrange v))ˣ], Function.Bijective ⇑(algebraMap O F)

Defined in: Mathlib.RingTheory.Valuation.Integers
Cited by: 1 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrderedCommGroupWithZero CommRing Algebra Subsingleton

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement · cited by 4,706
Submonoidstatement · cited by 3,086
Unitsstatement and proof · cited by 2,804
Units.valproof · cited by 1,966
map_zeroproof · cited by 1,614
eq_or_neproof · cited by 1,117
Function.Bijectivestatement · cited by 863

Cited by1

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Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrderedproof · cited by 1