Theorems · Theorem · field theory
minpoly.prime
∀ {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 → Prime (minpoly A x)A minimal polynomial is prime.
- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.zero_mulproof · cited by 1,625
- map_mulproof · cited by 1,137
- Polynomial.aevalproof · cited by 615
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
- Primestatement · cited by 277
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