Theorems · Theorem · commutative algebra
Ideal.IsMaximal.mem_pow_mul
∀ {R : Type u_2} [inst : CommSemiring R] (I : Ideal R) [I.IsMaximal] {a b : R} {n : ℕ},
a * b ∈ I ^ n → a ∈ I ^ n ∨ b ∈ ISee also Ideal.IsPrime.mem_pow_mul for prime ideal in Dedekind domain.
- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIdeal.IsMaximal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- mul_commproof · cited by 2,262
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.IsMaximal.mul_mem_powproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.