Theorems · Theorem · commutative algebra

Ideal.eq_prime_pow_of_succ_lt_of_le

∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] {P I : Ideal A} [P_prime : P.IsPrime],
  P ≠ ⊥ → ∀ {i : ℕ}, P ^ (i + 1) < I → I ≤ P ^ i → I = P ^ i

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainIdeal.IsPrime