nonUnitalNormedCommRing — Mathlib

English

A non-unital seminormed ring has a continuous multiplication operation with respect to its norm.

Русский

У нетривиального неполного нормированного кольца существует непрерывное умножение относительно норм.

LaTeX

$$$ \\text{ContinuousMul}(\\alpha) \\text{ given by } \\|xy\\| \\le \\|x\\| \\|y\\|.$$$

Lean4

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

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