Theorems · Theorem · commutative algebra
Ideal.IsMaximal.exists_inv_pow
∀ {R : Type u} [inst : CommSemiring R] (I : Ideal R) [I.IsMaximal] {x : R},
x ∉ I → ∀ (n : ℕ), ∃ y, ∃ i ∈ I ^ n, y * x + i = 1Generalize Ideal.IsMaximal.exists_inv to power of maximal ideals.
- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites13
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_oneproof · cited by 3,885
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- add_commproof · cited by 1,535
- pow_zeroproof · cited by 1,094
- Ideal.IsMaximalstatement and proof · cited by 452
- mul_addproof · cited by 413
- Ideal.pow_mem_powproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.IsMaximal.mul_mem_powproof · cited by 3