Theorems · Definition · commutative algebra
MulRingNorm.mulRingNormEquivAbsoluteValue
{R : Type u_2} → [inst : Ring R] → [Nontrivial R] → MulRingNorm R ≃ AbsoluteValue R ℝThe equivalence of MulRingNorm R and AbsoluteValue R ℝ when R is a nontrivial ring.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Equivstatement · cited by 8,337
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- AbsoluteValuestatement and proof · cited by 363
- AddGroupSeminorm.toFunproof · cited by 47
- MulHom.toFunproof · cited by 36
- MulRingNormstatement and proof · cited by 16
- MulRingSeminorm.toAddGroupSeminormproof · cited by 14
- MulRingNorm.toMulRingSeminormproof · cited by 9
- AbsoluteValue.toMulHomproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- spectralNorm_unique_field_norm_extproof · cited by 0
- MulRingNorm.mulRingNormEquivAbsoluteValue_applystatement · cited by 0
- MulRingNorm.mulRingNormEquivAbsoluteValue_symm_applystatement · cited by 0
- MulRingNorm.mulRingNormEquivAbsoluteValue.congr_simpstatement and proof · cited by 0