Theorems · Theorem · field theory
minpoly.ne_zero_of_finite
∀ (A : Type u_1) {B : Type u_2} [inst : Field A] [inst_1 : Ring B] [inst_2 : Algebra A B] (e : B)
[FiniteDimensional A B], minpoly A e ≠ 0- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- FiniteDimensionalstatement and proof · cited by 1,854
- minpolystatement · cited by 439
- minpoly.ne_zeroproof · cited by 44
- IsIntegral.of_finiteproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Module.End.exists_isNilpotent_isSemisimpleproof · cited by 3
- Module.AEval.isTorsion_of_finiteDimensionalproof · cited by 0
- Field.primitive_element_iff_minpoly_degree_eqproof · cited by 0