Theorems · Theorem · commutative algebra
Squarefree.ne_zero
∀ {R : Type u_1} [inst : MonoidWithZero R] [Nontrivial R] {m : R}, Squarefree m → m ≠ 0- Defined in
- Mathlib.Algebra.Squarefree.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZeroNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- MonoidWithZerostatement and proof · cited by 456
- Squarefreestatement and proof · cited by 112
- not_squarefree_zeroproof · cited by 1
Cited by18
Results whose statement or proof uses this declaration.
- Nat.prod_primeFactors_of_squarefreeproof · cited by 7
- Module.End.isSemisimple_of_squarefree_aeval_eq_zeroproof · cited by 4
- BoundingSieve.prodPrimes_ne_zeroproof · cited by 4
- Squarefree.dvd_of_squarefree_of_mul_dvd_mul_rightproof · cited by 2
- PerfectField.separable_iff_squarefreeproof · cited by 2
- ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_threeproof · cited by 2
- Nat.primeFactors_div_gcdproof · cited by 1
- ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefreeproof · cited by 1
- Squarefree.nodup_primeFactorsListproof · cited by 1
- IsRelPrime.moebius_mulproof · cited by 0
- Nat.Squarefree.ext_iffproof · cited by 0