Theorems · Theorem · commutative algebra
IsIntegrallyClosed.pow_dvd_pow_iff
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [IsIntegrallyClosed R] {n : ℕ},
n ≠ 0 → ∀ {a b : R}, a ^ n ∣ b ^ n ↔ a ∣ b- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- sub_selfproof · cited by 996
- map_powproof · cited by 503
- IsIntegralproof · cited by 427
- zero_powproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- Associated.pow_iffproof · cited by 0
- fermatLastTheoremWith'_polynomialproof · cited by 0