Theorems · Theorem · commutative algebra
Ring.ordMonoidWithZeroHom_eq_intValuation
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {x : R},
x ∈ nonZeroDivisors R → (Ring.ordMonoidWithZeroHom R) x = ((IsDiscreteValuationRing.maximalIdeal R).intValuation x)⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- MonoidWithZeroHomstatement · cited by 704
- WithZerostatement · cited by 586
- inv_invproof · cited by 494
- Multiplicative.ofAddproof · cited by 237
- WithZero.coeproof · cited by 186
Cited by1
Results whose statement or proof uses this declaration.
- Ring.ordFrac_eq_intValuationproof · cited by 1