Theorems · Theorem · commutative algebra
Polynomial.exists_irreducible_of_degree_pos
∀ {R : Type u_1} [inst : CommSemiring R] [NoZeroDivisors R] [WfDvdMonoid R] {f : Polynomial R} [Nontrivial R],
0 < f.degree → ∃ g, Irreducible g ∧ g ∣ f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- IsUnitproof · cited by 1,602
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- ne_of_gtproof · cited by 637
- NoZeroDivisorsstatement and proof · cited by 545
- Irreduciblestatement · cited by 496
- WithBot.bot_lt_coeproof · cited by 37
- WfDvdMonoidstatement and proof · cited by 37
- Polynomial.degree_zeroproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.exists_irreducible_of_natDegree_posproof · cited by 1