Theorems · Theorem · commutative algebra

IsFractionRing.of_field

∀ (R : Type u_1) [inst : CommRing R] (K : Type u_5) [inst_1 : Field K] [inst_2 : Algebra R K] [FaithfulSMul R K],
  (∀ (z : K), ∃ x y, z = (algebraMap R K) x / (algebraMap R K) y) → IsFractionRing R K

Defined in

Mathlib.RingTheory.Localization.FractionRing

Cited by

0 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraFaithfulSMul