Documentation

Mathlib.RingTheory.RingHom.Integral

The meta properties of integral ring homomorphisms. #

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theorem RingHom.isIntegral_stableUnderComposition :
StableUnderComposition fun {R S : Type u_1} [CommRing R] [CommRing S] (f : R →+* S) => f.IsIntegral
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theorem RingHom.isIntegral_respectsIso :
RespectsIso fun {R S : Type u_1} [CommRing R] [CommRing S] (f : R →+* S) => f.IsIntegral
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theorem RingHom.isIntegral_isStableUnderBaseChange :
IsStableUnderBaseChange fun {R S : Type u_1} [CommRing R] [CommRing S] (f : R →+* S) => f.IsIntegral
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theorem RingHom.isIntegral_ofLocalizationSpan :
OfLocalizationSpan fun {R S : Type u_1} [CommRing R] [CommRing S] (x : R →+* S) => x.IsIntegral

S is an integral R-algebra if there exists a set { r } that spans R such that each Sᵣ is an integral Rᵣ-algebra.