Theorems · Theorem · commutative algebra
normalize_idem
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] (x : α),
normalize (normalize x) = normalize x- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Units.valproof · cited by 1,966
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement · cited by 137
- NormalizationMonoid.normUnitproof · cited by 33
- normUnit_mul_normUnitproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalize_normalized_factorproof · cited by 9
- Ideal.exists_normalized_span_of_isPrincipalproof · cited by 1
- UniqueFactorizationMonoid.prod_normalizedFactors_eqproof · cited by 1
- Associates.normalize_outproof · cited by 0