Theorems · Theorem · group theory
Associated.irreducible
∀ {M : Type u_1} [inst : Monoid M] {p q : M}, Associated p q → Irreducible p → Irreducible q- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- Irreduciblestatement and proof · cited by 496
- Associatedstatement and proof · cited by 296
- Associated.symmproof · cited by 87
- Irreducible.not_isUnitproof · cited by 42
- Irreducible.isUnit_or_isUnitproof · cited by 28
- Units.mul_inv_cancel_rightproof · cited by 20
- Units.inv_mul_cancel_rightproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- minpoly.eq_of_irreducibleproof · cited by 8
- Polynomial.exists_monic_irreducible_factorproof · cited by 3
- X_pow_sub_C_irreducible_of_primeproof · cited by 2
- Associated.irreducible_iffproof · cited by 2
- WfDvdMonoid.not_isUnit_iff_exists_factors_eqproof · cited by 2
- Polynomial.irreducible_compproof · cited by 1
- Polynomial.X_pow_sub_X_sub_one_irreducibleproof · cited by 1
- Polynomial.irreducible_of_dvd_cyclotomic_of_natDegreeproof · cited by 1
- Polynomial.X_pow_sub_X_sub_one_irreducible_ratproof · cited by 0