Theorems · Theorem · commutative algebra
Prime.ne_zero
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p : M}, Prime p → p ≠ 0- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
Cited by47
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- dvd_prime_powproof · cited by 6
- UniqueFactorizationMonoid.zero_notMem_normalizedFactorsproof · cited by 5
- Associated.primeproof · cited by 4
- Ideal.eq_prime_pow_mul_coprimeproof · cited by 3
- IsDedekindDomain.inf_pow_eq_prod_of_primeproof · cited by 3
- Prime.left_dvd_or_dvd_right_of_dvd_mulproof · cited by 3
- prime_factors_uniqueproof · cited by 3
- Ideal.eq_span_singleton_of_height_eq_oneproof · cited by 2
- Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvdproof · cited by 2
- UniqueFactorizationMonoid.prime_pow_coprime_prod_of_coprime_insertproof · cited by 2
- map_prime_of_factor_orderIsoproof · cited by 2