Theorems · Theorem · field theory
Polynomial.not_isUnit_of_natDegree_pos
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] (p : Polynomial R), 0 < p.natDegree → ¬IsUnit p- Defined in
- Mathlib.Algebra.Polynomial.Degree.Units
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- IsUnitstatement · cited by 1,602
- Polynomial.natDegreestatement and proof · cited by 1,105
- NoZeroDivisorsstatement and proof · cited by 545
- Polynomial.natDegree_pos_iff_degree_posproof · cited by 22
- Polynomial.not_isUnit_of_degree_posproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_oneproof · cited by 1
- Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_one_or_two_mulproof · cited by 1
- Polynomial.X_pow_sub_C_separable_iffproof · cited by 1
- Polynomial.irreducible_of_dvd_cyclotomic_of_natDegreeproof · cited by 1
- Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_one_mul_isMonicOfDegreeproof · cited by 0