Theorems · Theorem · commutative algebra
exists_squarefree_dvd_pow_of_ne_zero
∀ {R : Type u_1} [inst : CommMonoidWithZero R] [UniqueFactorizationMonoid R] {x : R},
x ≠ 0 → ∃ y n, Squarefree y ∧ y ∣ x ∧ x ∣ y ^ n- Defined in
- Mathlib.Algebra.Squarefree.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- IsUnitproof · cited by 1,602
- LT.lt.ne'proof · cited by 1,417
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- pow_oneproof · cited by 894
- Irreducibleproof · cited by 496
- pow_succproof · cited by 374
- UniqueFactorizationMonoidstatement and proof · cited by 279
- mul_powproof · cited by 220
- Squarefreestatement and proof · cited by 112
- dvd_mul_rightproof · cited by 89
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.exists_isNilpotent_isSemisimpleproof · cited by 3