Theorems · Theorem · field theory
Polynomial.Monic.prime_of_degree_eq_one
∀ {R : Type u} [inst : CommRing R] [IsDomain R] {p : Polynomial R}, p.degree = 1 → p.Monic → Prime p- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotstatement · cited by 1,498
- Polynomial.coeffproof · cited by 1,045
- map_oneproof · cited by 861
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.Monicstatement and proof · cited by 461
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.prime_of_degree_eq_oneproof · cited by 1
- Polynomial.Monic.irreducible_of_degree_eq_oneproof · cited by 0