Theorems · Theorem · commutative algebra
Polynomial.Monic.isPrimitive
∀ {R : Type u_1} [inst : CommSemiring R] {p : Polynomial R}, p.Monic → p.IsPrimitive- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.coeff_C_mulproof · cited by 55
- IsUnit.of_mul_eq_oneproof · cited by 43
- Polynomial.IsPrimitivestatement · cited by 33
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic.isPrimitiveproof · cited by 2
- Polynomial.Monic.irreducible_iff_irreducible_map_fraction_mapproof · cited by 2
- IsPrimitiveRoot.minpoly_eq_powproof · cited by 1
- Polynomial.X_pow_sub_X_sub_one_irreducible_ratproof · cited by 0