Theorems · Theorem · group theory
Associated.prime
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p q : M}, Associated p q → Prime p → Prime q- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- Primestatement and proof · cited by 277
- Prime.ne_zeroproof · cited by 47
- Prime.not_isUnitproof · cited by 29
- Units.mul_inv_cancel_rightproof · cited by 20
- Prime.dvd_or_dvdproof · cited by 17
- Associated.ne_zero_iffproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Associated.prime_iffproof · cited by 3
- Polynomial.prime_of_degree_eq_oneproof · cited by 1
- IsCyclotomicExtension.Rat.zeta_sub_one_dvd_intCast_iffproof · cited by 1
- prime_mul_iffproof · cited by 0