Theorems · Theorem · commutative algebra
Irreducible.not_isUnit
∀ {M : Type u_1} [inst : Monoid M] {p : M}, Irreducible p → ¬IsUnit pAn irreducible element is not a unit.
- Defined in
- Mathlib.Algebra.Group.Irreducible.Defs
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- IsUnitstatement · cited by 1,602
- Irreduciblestatement and proof · cited by 496
Cited by42
Results whose statement or proof uses this declaration.
- Nat.prime_iffproof · cited by 20
- Associated.irreducibleproof · cited by 10
- Irreducible.dvd_symmproof · cited by 9
- Irreducible.natDegree_posproof · cited by 8
- Irreducible.associated_of_dvdproof · cited by 6
- irreducible_iffproof · cited by 5
- WfDvdMonoid.induction_on_irreducibleproof · cited by 5
- Polynomial.not_irreducible_Cproof · cited by 5
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- PrincipalIdealRing.isMaximal_of_irreducibleproof · cited by 4
- Irreducible.isRelPrime_iff_not_dvdproof · cited by 4
- Irreducible.of_mapproof · cited by 4