Theorems · Theorem · functional analysis
MulAlgebraNorm.extends_norm
∀ {R : outParam (Type u_1)} {S : outParam (Type u_2)} [inst : SeminormedCommRing R] [inst_1 : Ring S]
[inst_2 : Algebra R S] (f : MulAlgebraNorm R S) (a : R), f ((algebraMap R S) a) = ‖a‖A multiplicative R-algebra norm extends the norm on R.
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- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- Realstatement · cited by 25,697
- Algebrastatement and proof · cited by 11,388
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- Ringstatement and proof · cited by 7,463
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- SeminormedCommRingstatement and proof · cited by 38
- MulAlgebraNormstatement and proof · cited by 15
- MulAlgebraNorm.extends_norm'proof · cited by 1
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