Theorems · Inductive type · commutative algebra
MulRingSeminorm
(R : Type u_2) → [NonAssocRing R] → Type u_2
A multiplicative seminorm on a ring R is a function f : R → ℝ that preserves zero and
multiplication, takes nonnegative values, is subadditive and such that f (-x) = f x for all x.
- Cited by
- 12 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 by26
Results whose statement or proof uses this declaration.
- MulRingSeminorm.toAddGroupSeminormstatement and proof · cited by 14
- MulRingNorm.toMulRingSeminormstatement · cited by 9
- MulRingSeminorm.map_one'statement and proof · cited by 1
- MulRingNorm.mk.injstatement and proof · cited by 1
- MulRingNorm.mk.noConfusionstatement and proof · cited by 1
- MulRingSeminorm.mk.injstatement · cited by 1
- MulRingSeminorm.mk.noConfusionstatement · cited by 1
- MulRingSeminorm.extstatement and proof · cited by 1
- MulRingSeminorm.map_mul'statement and proof · cited by 0
- MulRingSeminorm.noConfusionstatement and proof · cited by 0
- MulRingSeminorm.noConfusionTypestatement and proof · cited by 0
- MulRingSeminorm.recOnstatement and proof · cited by 0