Theorems · Theorem · commutative algebra

IsFractionRing.semilinearEquivOfRingEquiv_comp

∀ {A : Type u_8} {B : Type u_9} (K : Type u_10) (L : Type u_11) [inst : CommRing A] [inst_1 : CommRing B]
  [inst_2 : CommRing K] [inst_3 : CommRing L] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K]
  [inst_6 : Algebra B L] [inst_7 : IsFractionRing B L] (f : A ≃+* B) {C : Type u_12} (M : Type u_13)
  [inst_8 : CommRing C] [inst_9 : CommRing M] [inst_10 : Algebra C M] [inst_11 : IsFractionRing C M] (g : B ≃+* C),
  have this := ⋯;
  have this_1 := ⋯;
  IsFractionRing.semilinearEquivOfRingEquiv K M (f.trans g) =
    (IsFractionRing.semilinearEquivOfRingEquiv K L f).trans (IsFractionRing.semilinearEquivOfRingEquiv L M g)

Defined in

Mathlib.RingTheory.Localization.FractionRing

Cited by

1 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingCommRingAlgebraIsFractionRingAlgebraIsFractionRingCommRingCommRingAlgebraIsFractionRing