Theorems · Theorem · commutative algebra
Irreducible.isPrimitive
∀ {R : Type u_1} [inst : CommSemiring R] [NoZeroDivisors R] {p : Polynomial R},
Irreducible p → p.natDegree ≠ 0 → p.IsPrimitiveAn irreducible nonconstant polynomial over a domain is primitive.
- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- IsUnitproof · cited by 1,602
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- NoZeroDivisorsstatement and proof · cited by 545
- Irreduciblestatement and proof · cited by 496
- IsUnit.mapproof · cited by 104
- Polynomial.natDegree_Cproof · cited by 59
Cited by2
Results whose statement or proof uses this declaration.
- exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_powproof · cited by 2
- RatFunc.irreducible_minpolyXproof · cited by 1