of_finite — Mathlib

English

If R and S are rings with R Noetherian and S finite over R in a tower, then S is Noetherian.

Русский

Если R и S кольца, R Ноетерово, а S конечно над R в цилиндре-теле, то S Ноетерна.

LaTeX

$$$IsNoetherianRing(R) \land Module.Finite(R,S) \Rightarrow IsNoetherianRing(S)$$$

Lean4

theorem of_finite (R S) [Ring R] [Ring S] [Module R S] [IsScalarTower R S S] [IsNoetherianRing R] [Module.Finite R S] :
    IsNoetherianRing S :=
  isNoetherian_of_tower R inferInstance

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