Theorems · Definition · functional analysis

MulAlgebraNorm.toAlgebraNorm

{R : outParam (Type u_1)} →
  {S : outParam (Type u_2)} →
    [inst : SeminormedCommRing R] → [inst_1 : Ring S] → [inst_2 : Algebra R S] → MulAlgebraNorm R S → AlgebraNorm R S

The algebra norm underlying an multiplicative algebra norm.

Defined in: Mathlib.Analysis.Normed.Unbundled.AlgebraNorm
Cited by: 1 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedCommRing Ring Algebra

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Algebrastatement and proof · cited by 11,388
Ringstatement and proof · cited by 7,463
AlgebraNormstatement · cited by 39
SeminormedCommRingstatement and proof · cited by 38
MulAlgebraNormstatement and proof · cited by 15
MulRingSeminorm.toAddGroupSeminormproof · cited by 14
MulRingNorm.toMulRingSeminormproof · cited by 9
MulAlgebraNorm.toMulRingNormproof · cited by 4
MulAlgebraNorm.smul'proof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

MulAlgebraNorm.coe_AlgebraNormstatement · cited by 1