Theorems · Theorem · commutative algebra
Commute.pow_dvd_add_pow_of_pow_eq_zero_right
∀ {R : Type u_1} {x y : R} {n m p : ℕ} [inst : Semiring R],
n + m ≤ p + 1 → Commute x y → y ^ n = 0 → x ^ m ∣ (x + y) ^ p- Defined in
- Mathlib.Algebra.Ring.Divisibility.Lemmas
- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- MulZeroClass.mul_zeroproof · cited by 2,091
- Commutestatement and proof · cited by 639
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- le_or_gtproof · cited by 269
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- pow_dvd_powproof · cited by 56
- dvd_mul_of_dvd_leftproof · cited by 25
- Finset.dvd_sumproof · cited by 11
- pow_eq_zero_of_leproof · cited by 9
- Commute.add_pow'proof · cited by 6
- dvd_nsmul_of_dvdproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Commute.pow_dvd_add_pow_of_pow_eq_zero_leftproof · cited by 1