normedAlgebra — Mathlib

English

A detailed lemma about the commutativity of scalar action in Pi-normed algebras.

Русский

Подробная лемма о коммутативности действия скаляра в Pi-нормированных алгебрах.

LaTeX

$$$\\forall a\\in 𝕜, \\forall b\\in \\Pi_i E_i, a \\cdot b = b \\cdot a$$$

Lean4

/-- The product of finitely many normed algebras is a normed algebra, with the sup norm. -/
instance normedAlgebra {ι : Type*} {E : ι → Type*} [Fintype ι] [∀ i, SeminormedRing (E i)]
    [∀ i, NormedAlgebra 𝕜 (E i)] : NormedAlgebra 𝕜 (∀ i, E i) :=
  { Pi.normedSpace, Pi.algebra _ E with }

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