seminormedCommRing — Mathlib

English

A subalgebra of a seminormed commutative ring is itself a seminormed commutative ring under the restricted norm.

Русский

Подалгебра семинормированного кольца остаётся семинарномерным коммутативным кольцом при ограничении нормы.

LaTeX

$$$\text{If } s \le E \text{ is a subalgebra, then } s \text{ is a SeminormedCommRing with restricted norm.}$$$

Lean4

/-- A subalgebra of a seminormed commutative ring is also a seminormed commutative ring, with the
restriction of the norm. -/
instance seminormedCommRing {𝕜 : Type*} [CommRing 𝕜] {E : Type*} [SeminormedCommRing E] [Algebra 𝕜 E]
    (s : Subalgebra 𝕜 E) : SeminormedCommRing s :=
  { s.seminormedRing, s.toCommRing with }

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