Theorems · Inductive type · commutative algebra
MulRingNorm
(R : Type u_2) → [NonAssocRing R] → Type u_2
A multiplicative norm on a ring R is a multiplicative ring seminorm such that f x = 0
implies x = 0.
It is recommended to use AbsoluteValue R ℝ instead (which works for Semiring R
and is equivalent to MulRingNorm R for a nontrivial Ring R).
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- NonAssocRing
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.
- NonAssocRingstatement · cited by 483
Cited by34
Results whose statement or proof uses this declaration.
- MulRingNorm.toMulRingSeminormstatement and proof · cited by 9
- MulAlgebraNorm.toMulRingNormstatement · cited by 4
- MulRingNorm.mulRingNormEquivAbsoluteValuestatement and proof · cited by 4
- NormedField.toMulRingNormstatement · cited by 2
- MulRingNorm.isPowMulstatement and proof · cited by 2
- NormedAlgebra.toMulAlgebraNormproof · cited by 2
- MulRingNorm.mk.injstatement · cited by 1
- MulRingNorm.mk.noConfusionstatement · cited by 1
- MulAlgebraNorm.mk.injstatement and proof · cited by 1
- MulAlgebraNorm.mk.noConfusionstatement and proof · cited by 1
- MulRingNorm.eq_zero_of_map_eq_zero'statement and proof · cited by 1
- MulRingNorm.extstatement and proof · cited by 1