Theorems · Definition · commutative algebra
RingSeminorm.toRingNorm
{K : Type u_2} → [inst : Field K] → (f : RingSeminorm K) → f ≠ 0 → RingNorm KA nonzero ring seminorm on a field K is a ring norm.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- RingSeminormstatement and proof · cited by 58
- AddGroupSeminorm.toFunproof · cited by 47
- RingSeminorm.toAddGroupSeminormproof · cited by 16
- RingNormstatement · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5
- RingSeminorm.toRingNorm.congr_simpstatement and proof · cited by 1
- normFromConstproof · cited by 1