Theorems · Theorem · commutative algebra

FractionalIdeal.map_ne_zero

∀ {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], I ≠ 0 → FractionalIdeal.map h I ≠ 0

Defined in

Mathlib.RingTheory.FractionalIdeal.Operations

Cited by

2 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldFieldAlgebraIsFractionRingAlgebraIsFractionRingNontrivial