Theorems · Theorem · commutative algebra
Squarefree.isRadical
∀ {R : Type u_1} [inst : CommMonoidWithZero R] [DecompositionMonoid R] {x : R}, Squarefree x → IsRadical x- Defined in
- Mathlib.Algebra.Squarefree.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- sqproof · cited by 280
- Squarefreestatement and proof · cited by 112
- one_lt_twoproof · cited by 67
- DecompositionMonoidstatement and proof · cited by 39
- IsRadicalstatement · cited by 16
- exists_dvd_and_dvd_of_dvd_mulproof · cited by 6
- isRadical_iff_pow_one_ltproof · cited by 3
- IsRelPrime.mul_dvdproof · cited by 2
- IsRelPrime.of_squarefree_mulproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Module.End.isSemisimple_of_squarefree_aeval_eq_zeroproof · cited by 4
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- Squarefree.dvd_of_squarefree_of_mul_dvd_mul_rightproof · cited by 2
- isRadical_iff_squarefree_of_ne_zeroproof · cited by 1
- isRadical_iff_squarefree_or_zeroproof · cited by 1
- IsPrimitiveRoot.minpoly_dvd_mod_pproof · cited by 1
- Squarefree.dvd_pow_iff_dvdproof · cited by 0