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Theorems · Theorem · commutative algebra

isIntegral_of_noetherian

∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B],
  IsNoetherian R B → ∀ (x : B), IsIntegral R x
Defined in
Mathlib.RingTheory.IntegralClosure.Algebra.Basic
Cited by
2 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingRingAlgebra
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Around this declaration

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

spectrum.nonempty_of_isAlgClosed_of_finiteDimensional · cited by 2spectrum.nonempty_of_isAl…IsGalois.of_separable_splitting_field_aux · cited by 0IsGalois.of_separable_spl…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463RingIsIntegral · cited by 427IsIntegralIsNoetherian · cited by 208IsNoetherianIsIntegral.of_finite · cited by 16IsIntegral.of_finiteisIntegral_of_noetherianCITED BYCITES

Cites6

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Cited by2

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