Theorems · Inductive type · commutative algebra
RingNorm
(R : Type u_2) → [NonUnitalNonAssocRing R] → Type u_2
A function f : R → ℝ is a norm on a (nonunital) ring if it is a seminorm and f x = 0
implies x = 0.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonUnitalNonAssocRingstatement · cited by 354
Cited by38
Results whose statement or proof uses this declaration.
- RingNorm.toRingSeminormstatement and proof · cited by 11
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5
- spectralNorm_uniqueproof · cited by 3
- AlgebraNorm.toRingNormstatement · cited by 3
- NormedRing.toRingNormstatement · cited by 2
- algNormFromConstproof · cited by 2
- RingSeminorm.toRingNormstatement · cited by 2
- normRingNormstatement · cited by 1
- RingNorm.extstatement and proof · cited by 1
- RingNorm.toNormedRingstatement and proof · cited by 1
- RingNorm.mk.injstatement · cited by 1
- RingNorm.mk.noConfusionstatement · cited by 1