nonUnitalNormedRing — Mathlib

English

ℤ carries a NormOneClass structure, i.e., the norm of 1 is 1 and the usual properties hold.

Русский

Целые числа образуют NormOneClass: нормa единицы равна единице и др. стандартные свойства сохраняются.

LaTeX

$$$ \\text{NormOneClass}(\\mathbb{Z}) \\text{ with } \\|m\\| = |m|.$$$

Lean4

/-- Normed ring structure on the product of finitely many non-unital normed rings, using the sup
norm. -/
instance nonUnitalNormedRing {R : ι → Type*} [Fintype ι] [∀ i, NonUnitalNormedRing (R i)] :
    NonUnitalNormedRing (∀ i, R i) :=
  { Pi.nonUnitalSeminormedRing, Pi.normedAddCommGroup with }

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