Theorems · Inductive type · commutative algebra
NormalizationMonoid
(α : Type u_2) → [MonoidWithZero α] → Type u_2
Normalization monoid: multiplying with normUnit gives a normal form for associated
elements.
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 165 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidWithZerostatement · cited by 456
Cited by198
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- normalizestatement and proof · cited by 137
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
- NormalizationMonoid.normUnitstatement and proof · cited by 33
- UniqueFactorizationMonoid.primeFactorsstatement and proof · cited by 32
- UniqueFactorizationMonoid.prime_of_normalized_factorstatement and proof · cited by 23
- UniqueFactorizationMonoid.prod_normalizedFactorsstatement and proof · cited by 23
- UniqueFactorizationMonoid.dvd_of_mem_normalizedFactorsstatement and proof · cited by 20
- normalize_zerostatement and proof · cited by 16
- Associates.outstatement and proof · cited by 15
- UniqueFactorizationMonoid.irreducible_of_normalized_factorstatement and proof · cited by 15
- dvd_antisymm_of_normalize_eqstatement and proof · cited by 15