Theorems · Theorem · commutative algebra
associated_normalize
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] (x : α), Associated x (normalize x)- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidWithZerostatement and proof · cited by 456
- Associatedstatement · cited by 296
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement · cited by 137
- NormalizationMonoid.normUnitproof · cited by 33
Cited by11
Results whose statement or proof uses this declaration.
- normalize_associatedproof · cited by 7
- normalize_eq_normalize_iff_associatedproof · cited by 5
- Multiset.gcd_dedupproof · cited by 4
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Multiset.lcm_dedupproof · cited by 3
- normalize_associated_iffproof · cited by 1
- IsGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipalproof · cited by 1
- normalize_eq_zeroproof · cited by 1
- Associates.out_mul'proof · cited by 0
- associated_normalize_iffproof · cited by 0