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Theorems · Theorem · commutative algebra

RingHom.IsIntegral.of_finite

∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S}, f.Finite → f.IsIntegral

Alias of RingHom.Finite.to_isIntegral. [Stacks Tag 00GK](https://stacks.math.columbia.edu/tag/00GK)

Defined in
Mathlib.RingTheory.IntegralClosure.Algebra.Basic
Cited by
1 results in Mathlib
Foundations
Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRing
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Around this declaration

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

Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐ · cited by 1Localization.exists_finit…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomRingHom.IsIntegral · cited by 54RingHom.IsIntegralRingHom.Finite · cited by 48RingHom.FiniteRingHom.Finite.to_isIntegral · cited by 3Finite.to_isIntegralIsIntegral.of_finiteCITED BYCITES

Cites5

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

Cited by1

Results whose statement or proof uses this declaration.