Theorems · Theorem · commutative algebra

IsAlmostIntegral.isIntegral_of_nonZeroDivisors_le_comap

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {s : S},
  IsAlmostIntegral R s →
    ∀ [IsNoetherianRing R], nonZeroDivisors R ≤ Submonoid.comap (algebraMap R S) (nonZeroDivisors S) → IsIntegral R s

Defined in: Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral
Cited by: 1 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra IsNoetherianRing

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

DFunLike.coeproof · cited by 62,936
RingHom.idproof · cited by 18,349
CommRingstatement and proof · cited by 17,173
Semiringproof · cited by 13,802
Algebrastatement and proof · cited by 11,388
LinearMapproof · cited by 10,215
RingHomstatement · cited by 10,189
SetLike.coeproof · cited by 8,199
Submoduleproof · cited by 7,192
Algebra.algebraMapstatement and proof · cited by 4,706
IsScalarTowerproof · cited by 3,896
mul_oneproof · cited by 3,885

Cited by1

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IsAlmostIntegral.isIntegralproof · cited by 1