Structures · Analysis
NonUnitalNormedCommRing
A non-unital normed commutative ring is a non-unital commutative ring endowed with a
norm which satisfies the inequality ‖x y‖ ≤ ‖x‖ ‖y‖.
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Shape
- One type argument · adds mul_comm
Extends2
Extended by2
Forgetful instances
Every NonUnitalNormedCommRing is also a
Provided automatically by
Concrete types that are instances10
- SeparationQuotient
- BoundedContinuousFunction
- RestrictScalars
- ContinuousMapZero
- ZeroAtInftyContinuousMap
- Subtype
- Prod
- ULift
- MulOpposite
- ContinuousMap
How is a type an instance?
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Assumed by15
- NonUnitalNormedCommRing.toNonUnitalNormedRing
- NonUnitalNormedCommRing.toNonUnitalCommRing
- MulOpposite.instNonUnitalNormedCommRing
- lp.nonUnitalNormedCommRing
- NonUnitalNormedCommRing.mul_comm
- NonUnitalSubalgebra.nonUnitalNormedCommRing
- NonUnitalNormedCommRing.induced
- BoundedContinuousFunction.instNonUnitalNormedCommRing
- Prod.nonUnitalNormedCommRing
- NonUnitalNormedCommRing.toNonUnitalSeminormedCommRing
- ContinuousMap.instNonUnitalNormedCommRing
- Pi.nonUnitalNormedCommRing
- ZeroAtInftyContinuousMap.instNonUnitalNormedCommRing
- ULift.nonUnitalNormedCommRing
- instNonUnitalNormedCommRingRestrictScalars
Ancestors93
- Add
- AddAction
- AddCancelCommMonoid
- AddCancelMonoid
- AddCommGroup
- AddCommMagma
- AddCommMonoid
- AddCommSemigroup
- AddGroup
- AddLeftCancelMonoid
- AddLeftCancelSemigroup
- AddMonoid
- AddRightCancelMonoid
- AddRightCancelSemigroup
- AddSemigroup
- AddSemigroupAction
- AddTorsor
- AddZero
- AddZeroClass
- AlgebraicGeometry.QuasiSeparated
- Bornology
- Bracket
- ChartedSpace
- CommMagma
- CommSemigroup
- CompactSpace
- CompactlyCoherentSpace
- Dist
- Distrib
- Dvd
- EDist
- EMetricSpace
- ENorm
- HAdd
- HMul
- HSMul
- HSub
- HVAdd
- InvolutiveNeg
- IsLeftCancelAdd
- IsRightCancelAdd
- Lean.Grind.AddCommGroup
- Lean.Grind.AddCommMonoid
- Lean.Grind.IntModule
- Lean.Grind.NatModule
- LocallyPathConnectedSpace
- MetricSpace
- Mul
- MulZeroClass
- NNDist
- NNNorm
- NSMul
- Neg
- NegZeroClass
- NonUnitalCommRing
- NonUnitalCommSemiring
- NonUnitalNonAssocCommRing
- NonUnitalNonAssocCommSemiring
- NonUnitalNonAssocRing
- NonUnitalNonAssocSemiring
- NonUnitalNormedRing
- NonUnitalRing
- NonUnitalSeminormedCommRing
- NonUnitalSeminormedRing
- NonUnitalSemiring
- Nonempty
- Norm
- NormedAddCommGroup
- NormedAddGroup
- OfNat
- One
- PrespectralSpace
- PseudoEMetricSpace
- PseudoMetricSpace
- QuasiSeparatedSpace
- SMul
- Semigroup
- SemigroupWithZero
- SeminormedAddCommGroup
- SeminormedAddGroup
- SequentialSpace
- Sub
- SubNegMonoid
- SubNegZeroMonoid
- SubtractionCommMonoid
- SubtractionMonoid
- TopologicalSpace
- Topology.IsGeneratedBy
- UniformSpace
- VAdd
- VSub
- ZSMul
- Zero