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Theorems · Theorem · commutative algebra

Algebra.EssFiniteType.isNoetherianRing

∀ (R : Type u_3) (S : Type u_4) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [Algebra.EssFiniteType R S] [IsNoetherianRing R], IsNoetherianRing S
Defined in
Mathlib.RingTheory.Localization.Submodule
Cited by
2 results in Mathlib
Foundations
Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraAlgebra.EssFiniteTypeIsNoetherianRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.QuasiFiniteAt.exists_basicOpen_eq_singleton · cited by 2QuasiFiniteAt.exists_basi…IsUnramifiedAt.of_liesOver_of_ne_bot · cited by 1IsUnramifiedAt.of_liesOve…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIsNoetherianRing · cited by 268IsNoetherianRingAlgebra.EssFiniteType · cited by 68Algebra.EssFiniteTypeAlgebra.FiniteType.isNoetherianRing · cited by 6FiniteType.isNoetherianRi…Algebra.EssFiniteType.subalgebra · cited by 5EssFiniteType.subalgebraAlgebra.EssFiniteType.submonoid · cited by 4EssFiniteType.submonoidIsLocalization.isNoetherianRing · cited by 4IsLocalization.isNoetheri…EssFiniteType.isNoetherianRingCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.