Theorems · Theorem · commutative algebra
Irreducible.squarefree
∀ {R : Type u_1} [inst : CommMonoid R] {x : R}, Irreducible x → Squarefree x- Defined in
- Mathlib.Algebra.Squarefree.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- Irreduciblestatement and proof · cited by 496
- Squarefreestatement · cited by 112
- Irreducible.isUnit_or_isUnitproof · cited by 28
- isUnit_of_mul_isUnit_leftproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- ArithmeticFunction.moebius_apply_primeproof · cited by 3
- exists_squarefree_dvd_pow_of_ne_zeroproof · cited by 1
- squarefree_primorialproof · cited by 0
- Irreducible.moebius_eqproof · cited by 0
- Nat.squarefree_and_prime_pow_iff_primeproof · cited by 0
- Prime.squarefreeproof · cited by 0