Theorems · Theorem · commutative algebra
Ideal.add_pow_mem_of_pow_mem_of_le_of_commute
∀ {α : Type u_6} [inst : Semiring α] (I : Ideal α) {a b : α} {m n k : ℕ},
a ^ m ∈ I → b ^ n ∈ I → m + n ≤ k + 1 → Commute a b → (a + b) ^ k ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Finset.sum_congrproof · cited by 2,323
- Finset.rangeproof · cited by 1,341
- Commutestatement and proof · cited by 639
- Nat.chooseproof · cited by 494
- Ideal.mul_mem_leftproof · cited by 107
- Submodule.sum_memproof · cited by 42
- Commute.pow_powproof · cited by 14
- Commute.add_powproof · cited by 12
- Ideal.pow_mem_of_pow_memproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.add_pow_add_pred_mem_of_pow_mem_of_commuteproof · cited by 1
- IsTopologicallyNilpotent.add_of_commuteproof · cited by 1
- Ideal.add_pow_mem_of_pow_mem_of_leproof · cited by 0