Theorems · Theorem · commutative algebra
Irreducible.prime
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [DecompositionMonoid M] {a : M}, Irreducible a → Prime a- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 496
- Primestatement · cited by 277
- DecompositionMonoidstatement and proof · cited by 39
- DecompositionMonoid.primalproof · cited by 5
- Irreducible.prime_of_isPrimalproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- irreducible_iff_primeproof · cited by 15
- Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx'_mulproof · cited by 2
- isCoprime_of_prime_dvdproof · cited by 1
- Ideal.IsDedekindDomain.emultiplicity_map_eq_zero_of_neproof · cited by 0