seminormedRing — Mathlib

English

The finite product of seminormed rings is again a seminormed ring with the sup norm, with the operations defined pointwise.

Русский

Конечное произведение полей с нормировкой является полугомром_RING выполнимый через максимум нормы по индексам.

LaTeX

$$$ \\text{There is a canonical } \\text{seminormedRing structure on } \\prod_{i=1}^n R_i \\text{ given by } \\|x\\|_\\infty = \\max_i \\|x_i\\|.$$$

Lean4

/-- Seminormed ring structure on the product of finitely many seminormed rings,
  using the sup norm. -/
instance seminormedRing {R : ι → Type*} [Fintype ι] [∀ i, SeminormedRing (R i)] : SeminormedRing (∀ i, R i) :=
  { Pi.nonUnitalSeminormedRing, Pi.ring with }

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