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Theorems · Theorem · commutative algebra

UniqueFactorizationMonoid.radical_one

∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M],
  UniqueFactorizationMonoid.radical 1 = 1
Defined in
Mathlib.RingTheory.Radical.Basic
Cited by
5 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizationMonoidUniqueFactorizationMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UniqueFactorizationMonoid.radical_of_isUnit · cited by 3UniqueFactorizationMonoid…UniqueFactorizationDomain.radical_neg_one · cited by 0UniqueFactorizationDomain…UniqueFactorizationMonoid.radical_pow_dvd · cited by 0UniqueFactorizationMonoid…UniqueFactorizationMonoid.radical_prod · cited by 0UniqueFactorizationMonoid…UniqueFactorizationMonoid.radical_prod_dvd · cited by 0UniqueFactorizationMonoid…CommMonoidWithZero · cited by 913CommMonoidWithZeroFinset.prod_congr · cited by 646Finset.prod_congrUniqueFactorizationMonoid · cited by 279UniqueFactorizationMonoidNormalizationMonoid · cited by 165NormalizationMonoidUniqueFactorizationMonoid.radical · cited by 64UniqueFactorizationMonoid…UniqueFactorizationMonoid.primeFactors_one · cited by 2UniqueFactorizationMonoid…UniqueFactorizationMonoid.rad…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.