Theorems · Theorem · commutative algebra
Irreducible.isCoprime_or_dvd
∀ {R : Type u} [inst : CommRing R] [IsBezout R] {p : R}, Irreducible p → ∀ (i : R), IsCoprime p i ∨ p ∣ i- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Irreduciblestatement and proof · cited by 496
- IsCoprimestatement and proof · cited by 321
- emproof · cited by 115
- IsBezoutstatement and proof · cited by 23
- Irreducible.dvd_iff_not_isCoprimeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_oneproof · cited by 1