Theorems · Definition · commutative algebra
Polynomial.IsPrimitive
{R : Type u_1} → [inst : CommSemiring R] → Polynomial R → PropA polynomial is primitive when the only constant polynomials dividing it are units. Note: This has nothing to do with minimal polynomials of primitive elements in finite fields.
- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 101 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.
Cites5
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
- IsUnitproof · cited by 1,602
- Polynomial.Cproof · cited by 1,598
Cited by33
Results whose statement or proof uses this declaration.
- Polynomial.IsPrimitive.content_eq_onestatement and proof · cited by 5
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapstatement and proof · cited by 4
- Polynomial.IsPrimitive.ne_zerostatement and proof · cited by 4
- Polynomial.isPrimitive_iff_content_eq_onestatement and proof · cited by 4
- Polynomial.isPrimitive_primPartstatement and proof · cited by 4
- Polynomial.Monic.isPrimitivestatement · cited by 4
- Polynomial.IsPrimitive.mulstatement and proof · cited by 3
- Polynomial.IsPrimitive.dvd_primPart_iff_dvdstatement and proof · cited by 2
- Polynomial.IsPrimitive.irreducible_of_irreducible_map_of_injectivestatement and proof · cited by 2
- Polynomial.IsPrimitive.isUnit_iff_isUnit_mapstatement and proof · cited by 2
- Polynomial.IsPrimitive.isUnit_iff_isUnit_map_of_injectivestatement and proof · cited by 2
- Polynomial.IsPrimitive.mul_map_mem_lifts_iffstatement and proof · cited by 2