Theorems · Theorem · commutative algebra
ModP.v_p_lt_val
∀ {K : Type u₁} [inst : Field K] {v : Valuation K NNReal} {O : Type u₂} [inst_1 : CommRing O] [inst_2 : Algebra O K],
v.Integers O → ∀ {p : ℕ} {x : O}, v ↑p < v ((algebraMap O K) x) ↔ (Ideal.Quotient.mk (Ideal.span {↑p})) x ≠ 0- Defined in
- Mathlib.RingTheory.Perfection
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Setstatement · cited by 53,352
- 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
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- NNRealstatement and proof · cited by 4,310
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.spanstatement and proof · cited by 948
- Valuationstatement and proof · cited by 823
Cited by1
Results whose statement or proof uses this declaration.
- ModP.mul_ne_zero_of_pow_p_ne_zeroproof · cited by 1