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Theorems · Theorem · commutative algebra

isRadical_iff_squarefree_of_ne_zero

∀ {R : Type u_1} [inst : CommMonoidWithZero R] [IsCancelMulZero R] {x : R} [DecompositionMonoid R],
  x ≠ 0 → (IsRadical x ↔ Squarefree x)
Defined in
Mathlib.Algebra.Squarefree.Basic
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroIsCancelMulZeroDecompositionMonoid
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Around this declaration

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UniqueFactorizationMonoid.normalizedFactors_nodup · cited by 2UniqueFactorizationMonoid…CommMonoidWithZero · cited by 913CommMonoidWithZeroIsCancelMulZero · cited by 177IsCancelMulZeroSquarefree · cited by 112SquarefreeDecompositionMonoid · cited by 39DecompositionMonoidIsRadical · cited by 16IsRadicalSquarefree.isRadical · cited by 7Squarefree.isRadicalIsRadical.squarefree · cited by 6IsRadical.squarefreeisRadical_iff_squarefree_of_n…CITED BYCITES

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Cited by1

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