Theorems · Inductive type · functional analysis
AlgebraNorm
(R : Type u_1) → [inst : SeminormedCommRing R] → (S : Type u_2) → [inst_1 : Ring S] → [Algebra R S] → Type u_2
An algebra norm on an R-algebra S is a ring norm on S compatible with the
action of R.
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement · cited by 11,388
- Ringstatement · cited by 7,463
- SeminormedCommRingstatement · cited by 38
Cited by57
Results whose statement or proof uses this declaration.
- spectralAlgNormstatement · cited by 9
- IsUltrametricDist.algNormOfAlgEquivstatement · cited by 7
- IsUltrametricDist.invariantExtensionstatement · cited by 6
- spectralMulAlgNormproof · cited by 5
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalstatement and proof · cited by 5
- spectralAlgNorm_of_finiteDimensional_normalstatement · cited by 4
- AlgebraNorm.toRingNormstatement and proof · cited by 3
- norm_root_le_spectralValuestatement and proof · cited by 3
- spectralAlgNorm_of_finiteDimensional_normal_defstatement · cited by 3
- spectralNorm_eq_invariantExtensionstatement and proof · cited by 3
- spectralNorm_uniquestatement and proof · cited by 3
- algNormFromConststatement · cited by 2