Theorems · Theorem · commutative algebra
Ideal.IsPrime.mem_pow_mul
∀ {R : Type u_1} [inst : CommRing R] [IsDedekindDomain R] (I : Ideal R) [hI : I.IsPrime] {a b : R} {n : ℕ},
a * b ∈ I ^ n → a ∈ I ^ n ∨ b ∈ ISee also Ideal.IsMaximal.mem_pow_mul for maximal ideal.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- mul_commproof · cited by 2,262
- Ideal.IsPrimestatement and proof · cited by 827
- IsDedekindDomainstatement and proof · cited by 668
- Ideal.IsPrime.mul_mem_powproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.quotientToQuotientRangePowQuotSucc_injectiveproof · cited by 0