Theorems · Theorem · commutative algebra

FractionalIdeal.map_eq_zero_iff

∀ {R : Type u_1} [inst : CommRing R] {K : Type u_3} {K' : Type u_4} [inst_1 : Field K] [inst_2 : Field K']
  [inst_3 : Algebra R K] [IsFractionRing R K] [inst_5 : Algebra R K'] [IsFractionRing R K']
  {I : FractionalIdeal (nonZeroDivisors R) K} (h : K →ₐ[R] K') [Nontrivial R], FractionalIdeal.map h I = 0 ↔ I = 0

Defined in

Mathlib.RingTheory.FractionalIdeal.Operations

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldFieldAlgebraIsFractionRingAlgebraIsFractionRingNontrivial