Theorems · Theorem · commutative algebra
Associated.eq_of_normalized
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] {a b : α},
Associated a b → normalize a = a → normalize b = b → a = b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 296
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement and proof · cited by 137
- normalize_eq_normalize_iff_associatedproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Finset.lcm_eq_prodproof · cited by 1
- Polynomial.content_mulproof · cited by 1
- UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrimeproof · cited by 1
- neg_gcdproof · cited by 0
- gcd_negproof · cited by 0