Theorems · Theorem · commutative algebra
normalize_eq_one
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] {x : α}, normalize x = 1 ↔ IsUnit x- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement and proof · cited by 137
- Units.isUnitproof · cited by 116
- NormalizationMonoid.normUnitproof · cited by 33
- normalize_coe_unitsproof · cited by 2
- Units.eq_inv_of_mul_eq_one_rightproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.isPrimitive_primPartproof · cited by 4
- Polynomial.isPrimitive_iff_content_eq_oneproof · cited by 4
- Polynomial.IsPrimitive.mulproof · cited by 3
- Polynomial.monic_normalizeproof · cited by 2
- Irreducible.gcd_eq_one_iffproof · cited by 2
- Finset.extract_gcd'proof · cited by 1
- Multiset.extract_gcd'proof · cited by 1
- Polynomial.exists_primitive_lcm_of_isPrimitiveproof · cited by 0
- fermatLastTheoremWith_of_fermatLastTheoremWith_coprimeproof · cited by 0