Theorems · Theorem · field theory
minpoly.not_isUnit
∀ (A : Type u_1) {B : Type u_2} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Algebra A B] (x : B) [Nontrivial B],
¬IsUnit (minpoly A x)A minimal polynomial is not a unit.
- Defined in
- Mathlib.FieldTheory.Minpoly.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 113 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Nontrivialstatement and proof · cited by 2,416
- IsUnitstatement and proof · cited by 1,602
- minpolystatement · cited by 439
- IsIntegralproof · cited by 427
- minpoly.monicproof · cited by 81
- RingHom.domain_nontrivialproof · cited by 20
- not_isUnit_zeroproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- minpoly.eq_of_irreducible_of_monicproof · cited by 9
- IsAdjoinRootMonic.minpoly_eqproof · cited by 1
- minpoly.IsIntegrallyClosed.isIntegral_iff_isUnit_leadingCoeffproof · cited by 0
- minpoly.primeproof · cited by 0