Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_mul_of_isUnit_right
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a u : M}, IsUnit u → UniqueFactorizationMonoid.radical (a * u) = UniqueFactorizationMonoid.radical a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- associated_mul_unit_leftproof · cited by 8
- UniqueFactorizationMonoid.radical_eq_of_associatedproof · cited by 4
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