Theorems · Theorem · commutative algebra
Ideal.pow_mem_of_pow_mem
∀ {α : Type u} [inst : Semiring α] (I : Ideal α) {a : α} {m n : ℕ}, a ^ m ∈ I → m ≤ n → a ^ n ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- add_commproof · cited by 1,535
- pow_addproof · cited by 315
- Ideal.mul_mem_leftproof · cited by 107
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.add_pow_mem_of_pow_mem_of_le_of_commuteproof · cited by 3
- MvPolynomial.toMvPowerSeries_uniformContinuousproof · cited by 2