isNoetherianRing — Mathlib

English

If A is a Noetherian ring, then the degree zero part 𝒜0 of a graded ring 𝒜 is also Noetherian.

Русский

Если A — noetherová кольцо, то нулевая степень 𝒜0 градуированной кольца 𝒜 также ноetherová.

LaTeX

$$$$ \text{If } A \text{ is Noetherian, then } 𝒜_0 \text{ is Noetherian.} $$$$

Lean4

/-- If the internally graded ring `A` is Noetherian, then `𝒜 0` is a Noetherian ring. -/
instance isNoetherianRing : IsNoetherianRing (𝒜 0) :=
  isNoetherianRing_of_surjective A (𝒜 0) (GradedRing.projZeroRingHom' 𝒜) (GradedRing.projZeroRingHom'_surjective 𝒜)

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