Theorems · Theorem · commutative algebra

FractionalIdeal.extendedHom_coeIdeal_eq_map

∀ {A : Type u_1} {K : Type u_2} (L : Type u_3) (B : Type u_4) [inst : CommRing A] [inst_1 : IsDomain A]
  [inst_2 : CommRing B] [inst_3 : IsDomain B] [inst_4 : Algebra A B] [inst_5 : Module.IsTorsionFree A B]
  [inst_6 : Field K] [inst_7 : Field L] [inst_8 : Algebra A K] [inst_9 : Algebra B L] [inst_10 : IsFractionRing A K]
  [inst_11 : IsFractionRing B L] (I : Ideal A), (FractionalIdeal.extendedHom L B) ↑I = ↑(Ideal.map (algebraMap A B) I)

Defined in

Mathlib.RingTheory.FractionalIdeal.Extended

Cited by

5 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainCommRingIsDomainAlgebraModule.IsTorsionFreeFieldFieldAlgebraAlgebraIsFractionRingIsFractionRing