Theorems · Theorem · commutative algebra
Prime.irreducible
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {p : M}, Prime p → Irreducible p- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement · cited by 496
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- dvd_rflproof · cited by 80
- Prime.ne_zeroproof · cited by 47
- right_ne_zero_of_mulproof · cited by 38
- dvd_mul_of_dvd_rightproof · cited by 29
- Prime.not_isUnitproof · cited by 29
- left_ne_zero_of_mulproof · cited by 27
- dvd_mul_of_dvd_leftproof · cited by 25
- mul_dvd_mul_iff_leftproof · cited by 24
Cited by54
Results whose statement or proof uses this declaration.
- Nat.prime_iffproof · cited by 20
- irreducible_iff_primeproof · cited by 15
- UniqueFactorizationMonoid.irreducible_of_normalized_factorproof · cited by 15
- UniqueFactorizationMonoid.irreducible_of_factorproof · cited by 13
- Polynomial.irreducible_Xproof · cited by 5
- Ideal.IsDedekindDomain.ramificationIdx'_eq_normalizedFactors_countproof · cited by 5
- Polynomial.irreducible_X_sub_Cproof · cited by 4
- IsDiscreteValuationRing.addVal_eq_top_iffproof · cited by 4
- Ideal.count_associates_factors_eqproof · cited by 4
- Prime.coprime_iff_not_dvdproof · cited by 3
- Prime.dvd_prime_iff_associatedproof · cited by 3
- IsDiscreteValuationRing.addVal_defproof · cited by 3