Theorems · Theorem · commutative algebra
Ideal.add_pow_add_pred_mem_of_pow_mem_of_commute
∀ {α : Type u_6} [inst : Semiring α] (I : Ideal α) {a b : α} {m n : ℕ},
a ^ m ∈ I → b ^ n ∈ I → Commute a b → (a + b) ^ (m + n - 1) ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
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
- le_reflproof · cited by 2,061
- Commutestatement and proof · cited by 639
- Ideal.add_pow_mem_of_pow_mem_of_le_of_commuteproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.add_pow_add_pred_mem_of_pow_memproof · cited by 0