Theorems · Theorem · commutative algebra

FractionalIdeal.divMod_spec

∀ {R : Type u_1} [inst : CommRing R] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra R K]
  [inst_3 : IsFractionRing R K] [inst_4 : IsDedekindDomain R] {a b c : FractionalIdeal (nonZeroDivisors R) K},
  a ≤ c → a ≠ 0 → b ≠ 0 → a + FractionalIdeal.spanSingleton (nonZeroDivisors R) (c.divMod b a) * b = c

Defined in

Mathlib.RingTheory.DedekindDomain.Factorization

Cited by

0 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraIsFractionRingIsDedekindDomain