Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_zero
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M],
UniqueFactorizationMonoid.radical 0 = 1- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.prod_congrproof · cited by 646
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- UniqueFactorizationMonoid.primeFactors_zeroproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.primeFactors_radicalproof · cited by 5
- UniqueFactorizationMonoid.radical_dvd_radicalproof · cited by 2
- Nat.radical_le_self_iffproof · cited by 1
- UniqueFactorizationMonoid.radical_mul_dvdproof · cited by 1
- UniqueFactorizationMonoid.radical_eq_one_iffproof · cited by 0
- natDegree_radical_leproof · cited by 0