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Theorems · Theorem · commutative algebra

RingHom.FaithfullyFlat.injective

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
  f.FaithfullyFlat → Function.Injective ⇑f
Defined in
Mathlib.RingTheory.RingHom.FaithfullyFlat
Cited by
1 results in Mathlib
Foundations
Depth 111 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.

AlgebraicGeometry.Flat.epi_of_flat_of_surjective · cited by 1Flat.epi_of_flat_of_surje…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomRingHom.toAlgebra · cited by 337RingHom.toAlgebraFaithfulSMul.algebraMap_injective · cited by 198FaithfulSMul.algebraMap_i…RingHom.FaithfullyFlat · cited by 25RingHom.FaithfullyFlatFaithfullyFlat.injectiveCITED BYCITES

Cites7

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Cited by1

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