Theorems · Theorem · field theory
Polynomial.degree_eq_zero_of_isUnit
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {p : Polynomial R} [Nontrivial R], IsUnit p → p.degree = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Units
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Nontrivialstatement and proof · cited by 2,416
- IsUnitstatement and proof · cited by 1,602
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- NoZeroDivisorsstatement and proof · cited by 545
- LE.le.antisymmproof · cited by 507
- IsUnit.ne_zeroproof · cited by 36
- Polynomial.natDegree_eq_zero_iff_degree_le_zeroproof · cited by 12
- Polynomial.natDegree_eq_zero_of_isUnitproof · cited by 5
- Polynomial.zero_le_degree_iffproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- Polynomial.degree_eq_one_of_irreducible_of_rootproof · cited by 7
- Polynomial.degree_coe_unitsproof · cited by 5
- Polynomial.isUnit_iff_degree_eq_zeroproof · cited by 3
- Polynomial.isLocalHom_expandproof · cited by 2
- Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_mapproof · cited by 1
- Polynomial.not_isUnit_of_degree_posproof · cited by 1
- Polynomial.exists_irreducible_of_degree_posproof · cited by 1
- IsPrimitiveRoot.minpoly_eq_powproof · cited by 1
- Polynomial.Monic.irreducible_iff_degree_ltproof · cited by 1
- Polynomial.generalizedEisensteinproof · cited by 1
- minpoly.prime_of_isIntegrallyClosedproof · cited by 1
- Ideal.jacobson_bot_polynomial_le_sInf_map_maximalproof · cited by 1