Theorems · Theorem · commutative algebra
normalize_eq
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : Subsingleton αˣ] (x : α), normalize x = x- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Unitsstatement and proof · cited by 2,804
- CommMonoidWithZerostatement and proof · cited by 913
- normalizestatement · cited by 137
Cited by26
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.factors_eq_normalizedFactorsproof · cited by 7
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Ideal.irreducible_pow_supproof · cited by 5
- Ideal.IsDedekindDomain.ramificationIdx'_eq_normalizedFactors_countproof · cited by 5
- Equiv.Perm.IsThreeCycle.orderOfproof · cited by 4
- Ideal.count_normalizedFactors_eqproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicityproof · cited by 2
- Ideal.irreducible_pow_sup_of_geproof · cited by 2
- Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx'_mulproof · cited by 2
- Ideal.count_associates_eqproof · cited by 2
- Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicityproof · cited by 2