Theorems · Theorem · commutative algebra
Commute.pow_dvd_add_pow_of_pow_eq_zero_left
∀ {R : Type u_1} {x y : R} {n m p : ℕ} [inst : Semiring R],
n + m ≤ p + 1 → Commute x y → x ^ n = 0 → y ^ m ∣ (x + y) ^ p- Defined in
- Mathlib.Algebra.Ring.Divisibility.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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
- add_commproof · cited by 1,535
- Commutestatement and proof · cited by 639
- Commute.symmproof · cited by 79
- Commute.pow_dvd_add_pow_of_pow_eq_zero_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Commute.pow_dvd_pow_of_sub_pow_eq_zeroproof · cited by 3