Theorems · Theorem · commutative algebra
Irreducible.ne_zero
∀ {M : Type u_1} [inst : MonoidWithZero M] {p : M}, Irreducible p → p ≠ 0- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Irreduciblestatement and proof · cited by 496
- MonoidWithZerostatement and proof · cited by 456
- not_irreducible_zeroproof · cited by 6
Cited by45
Results whose statement or proof uses this declaration.
- Nat.Prime.ne_zeroproof · cited by 109
- UniqueFactorizationMonoid.normalizedFactors_irreducibleproof · cited by 10
- minpoly.eq_of_irreducibleproof · cited by 8
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- Nat.not_prime_zeroproof · cited by 6
- IsAlgClosed.of_exists_rootproof · cited by 5
- Ideal.irreducible_pow_supproof · cited by 5
- Ring.ord_eq_addValproof · cited by 3
- Polynomial.natDegree_of_dvd_cyclotomic_of_irreducibleproof · cited by 3
- Polynomial.exists_monic_irreducible_factorproof · cited by 3
- IsDiscreteValuationRing.intValuation_maximalIdealproof · cited by 3
- Irreducible.exists_dvd_monic_irreducible_of_isIntegralproof · cited by 2