Theorems · Theorem · commutative algebra

FractionalIdeal.map_comp

∀ {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'] {P'' : Type u_4} [inst_5 : CommRing P'']
  [inst_6 : Algebra R P''] (I : FractionalIdeal S P) (g : P →ₐ[R] P') (g' : P' →ₐ[R] P''),
  FractionalIdeal.map (g'.comp g) I = FractionalIdeal.map g' (FractionalIdeal.map g I)

Defined in

Mathlib.RingTheory.FractionalIdeal.Operations

Cited by

2 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraCommRingAlgebra