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Theorems · Theorem · commutative algebra

FractionalIdeal.map_injective

∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
  {P' : Type u_3} [inst_3 : CommRing P'] [inst_4 : Algebra R P'] (f : P →ₐ[R] P'),
  Function.Injective ⇑f → Function.Injective (FractionalIdeal.map f)
Defined in
Mathlib.RingTheory.FractionalIdeal.Operations
Cited by
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Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebra
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DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraAlgHom · cited by 3236AlgHomSubmonoid · cited by 3086SubmonoidFractionalIdeal · cited by 423FractionalIdealFractionalIdeal.map · cited by 20FractionalIdeal.mapFractionalIdeal.ext · cited by 13FractionalIdeal.extFractionalIdeal.map_mem_map · cited by 1FractionalIdeal.map_mem_m…FractionalIdeal.map_injectiveCITED BYCITES

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