Theorems · Theorem · commutative algebra
EuclideanDomain.divRadical_ne_zero
∀ {E : Type u_1} [inst : EuclideanDomain E] [inst_1 : NormalizationMonoid E] [inst_2 : UniqueFactorizationMonoid E]
{a : E}, a ≠ 0 → EuclideanDomain.divRadical a ≠ 0- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- EuclideanDomainstatement and proof · cited by 124
- right_ne_zero_of_mulproof · cited by 38
- EuclideanDomain.divRadicalstatement · cited by 12
- EuclideanDomain.radical_mul_divRadicalproof · cited by 5
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