Theorems · Theorem · commutative algebra
Valuation.integer.integers
∀ {R : Type u} {Γ₀ : Type v} [inst : CommRing R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀),
v.Integers ↥v.integer- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Subtype.coe_injectiveproof · cited by 205
- Valuation.integerstatement and proof · cited by 68
- Valuation.Integersstatement · cited by 58
Cited by17
Results whose statement or proof uses this declaration.
- Irreducible.maximalIdeal_pow_eq_setOfPred_le_v_coe_powproof · cited by 3
- Valuation.exists_pow_Uniformizerproof · cited by 3
- Valuation.integer.coe_span_singleton_eq_setOfPred_le_v_coeproof · cited by 2
- Valuation.integer.v_irreducible_lt_oneproof · cited by 2
- Valuation.IsUniformizer.not_isUnitproof · cited by 2
- Irreducible.maximalIdeal_eq_setOfPred_le_v_coeproof · cited by 2
- Valuation.Integer.not_isUnit_iff_valuation_lt_oneproof · cited by 2
- Valuation.integer.v_irreducible_posproof · cited by 1
- Valuation.IsUniformizer.of_associatedproof · cited by 1
- Valued.integer.isPrincipalIdealRing_of_compactSpaceproof · cited by 1
- Valued.integer.norm_coe_unitproof · cited by 1
- Valued.integer.totallyBounded_iff_finite_residueFieldproof · cited by 1