Theorems · Theorem · commutative algebra
UniqueFactorizationDomain.radical_neg
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizationMonoid R] [inst_2 : UniqueFactorizationMonoid R] {a : R},
UniqueFactorizationMonoid.radical (-a) = UniqueFactorizationMonoid.radical a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 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.
- CommRingstatement and proof · cited by 17,173
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- Associated.rflproof · cited by 9
- Associated.neg_leftproof · cited by 6
- UniqueFactorizationMonoid.radical_eq_of_associatedproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationDomain.radical_neg_oneproof · cited by 0