Theorems · Theorem · commutative algebra
Prime.dvd_mul
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p : M}, Prime p → ∀ {a b : M}, p ∣ a * b ↔ p ∣ a ∨ p ∣ b- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
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.
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
- dvd_mul_of_dvd_rightproof · cited by 29
- dvd_mul_of_dvd_leftproof · cited by 25
- Prime.dvd_or_dvdproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.splits_mulproof · cited by 4
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- Prime.not_dvd_mulproof · cited by 0
- divisor_closure_eq_closureproof · cited by 0