Theorems · Theorem · field theory
minpoly.coeff_zero_eq_zero
∀ {A : Type u_1} {B : Type u_2} [inst : Field A] [inst_1 : Ring B] [IsDomain B] [inst_3 : Algebra A B] {x : B},
IsIntegral A x → ((minpoly A x).coeff 0 = 0 ↔ x = 0)The constant coefficient of the minimal polynomial of x is 0 if and only if x = 0.
- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
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- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- map_zeroproof · cited by 1,614
- Polynomial.coeffstatement and proof · cited by 1,045
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
- Polynomial.IsRootproof · cited by 152
- Polynomial.coeff_X_zeroproof · cited by 48
- minpoly.zeroproof · cited by 2
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