Structures · Analysis
NormedCommRing
A normed commutative ring is a 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 NormedCommRing is also a
Provided automatically by
Concrete types that are instances15
- Int
- Real
- SeparationQuotient
- BoundedContinuousFunction
- UniformSpace.Completion
- PadicInt
- TrivSqZeroExt
- RestrictScalars
- Subtype
- Prod
- ULift
- MulOpposite
- PUnit
- HasQuotient.Quotient
- ContinuousMap
How is a type an instance?
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Assumed by241
- LinearMap.polar
- StrongDual.polar
- deriv_fun_pow
- HasDerivAt.pow
- Finset.norm_prod_le
- LinearMap.polar_gc
- DifferentiableAt.fun_finsetProd
- HasFDerivAt.mul
- LinearMap.polar_antitone
- LinearMap.polar_singleton
- HasDerivWithinAt.fun_finsetProd
- multipliable_one_add_of_summable
- HasDerivAt.fun_finsetProd
- EulerProduct.eulerProduct_hasProd
- DifferentiableWithinAt.fun_finsetProd
- contDiffWithinAt_prod'
- hasStrictFDerivAt_exp_smul_const_of_mem_ball
- AnalyticAt.aeval_mvPolynomial
- hasStrictFDerivAt_finsetProd
- HasFDerivAt.finsetProd
- Summable.hasProdUniformlyOn_one_add
- Finset.analyticWithinAt_fun_prod
- HasMFDerivWithinAt.mul
- hasStrictFDerivAt_multiset_prod
- LinearMap.zero_mem_polar
- HasFDerivWithinAt.finsetProd
- hasFDerivAt_exp_smul_const_of_mem_ball
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum
- HasFDerivAt.pow
- hasFDerivAt_finsetProd
- HasFDerivWithinAt.pow
- HasFDerivWithinAt.mul
- DifferentiableOn.fun_finsetProd
- AnalyticOnNhd.eval_linearMap
- DifferentiableOn.finsetProd
- EulerProduct.eulerProduct_hasProd_mulIndicator
- hasFDerivAt_multiset_prod
- ContinuousMultilinearMap.norm_mkPiAlgebra
- HasDerivWithinAt.pow
- Ideal.toCharacterSpace
- Finset.analyticAt_fun_prod
- HasStrictFDerivAt.pow
- HasMFDerivWithinAt.prod
- HasStrictFDerivAt.mul
- Finset.norm_prod_le'
- hasStrictFDerivAt_exp_smul_const_of_mem_ball'
- derivWithin_fun_finsetProd
- HasStrictFDerivAt.finsetProd
- MDifferentiableWithinAt.prod
- deriv_pow
Ancestors128
- Add
- AddAction
- AddCancelCommMonoid
- AddCancelMonoid
- AddCommGroup
- AddCommGroupWithOne
- AddCommMagma
- AddCommMonoid
- AddCommMonoidWithOne
- AddCommSemigroup
- AddGroup
- AddGroupWithOne
- AddLeftCancelMonoid
- AddLeftCancelSemigroup
- AddMonoid
- AddMonoidWithOne
- AddRightCancelMonoid
- AddRightCancelSemigroup
- AddSemigroup
- AddSemigroupAction
- AddTorsor
- AddZero
- AddZeroClass
- AlgebraicGeometry.QuasiSeparated
- Bornology
- Bracket
- ChartedSpace
- CommMagma
- CommMonoid
- CommMonoidWithZero
- CommRing
- CommSemigroup
- CommSemiring
- CompactSpace
- CompactlyCoherentSpace
- Dist
- Distrib
- Dvd
- EDist
- EMetricSpace
- ENorm
- HAdd
- HMul
- HSMul
- HSub
- HVAdd
- Ideal.FiniteHeight
- IntCast
- InvolutiveNeg
- IsJacobsonRing
- IsLeftCancelAdd
- IsRightCancelAdd
- IsSemiprimaryRing
- Lean.Grind.AddCommGroup
- Lean.Grind.AddCommMonoid
- Lean.Grind.CommRing
- Lean.Grind.CommSemiring
- Lean.Grind.IntModule
- Lean.Grind.NatModule
- Lean.Grind.Ring
- Lean.Grind.Semiring
- LocallyPathConnectedSpace
- MetricSpace
- Monoid
- MonoidWithZero
- Mul
- MulAction
- MulOne
- MulOneClass
- MulZeroClass
- MulZeroOneClass
- NNDist
- NNNorm
- NPow
- NSMul
- NatCast
- Neg
- NegZeroClass
- NonAssocCommRing
- NonAssocCommSemiring
- NonAssocRing
- NonAssocSemiring
- NonUnitalCommRing
- NonUnitalCommSemiring
- NonUnitalNonAssocCommRing
- NonUnitalNonAssocCommSemiring
- NonUnitalNonAssocRing
- NonUnitalNonAssocSemiring
- NonUnitalNormedCommRing
- NonUnitalNormedRing
- NonUnitalRing
- NonUnitalSeminormedCommRing
- NonUnitalSeminormedRing
- NonUnitalSemiring
- Nonempty
- Norm
- NormedAddCommGroup
- NormedAddGroup
- NormedRing
- OfNat
- One
- PrespectralSpace
- PseudoEMetricSpace
- PseudoMetricSpace
- QuasiSeparatedSpace
- Ring
- SMul
- Semigroup
- SemigroupAction
- SemigroupWithZero
- SeminormedAddCommGroup
- SeminormedAddGroup
- SeminormedCommRing
- SeminormedRing
- Semiring
- SequentialSpace
- Sub
- SubNegMonoid
- SubNegZeroMonoid
- SubtractionCommMonoid
- SubtractionMonoid
- TopologicalSpace
- Topology.IsGeneratedBy
- UniformSpace
- VAdd
- VSub
- ZSMul
- Zero