Theorems · Theorem · field theory
Polynomial.Irreducible.natDegree_dvd_finrank
∀ {K : Type u} [inst : Field K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] {f : Polynomial K},
Irreducible f → (Polynomial.map (algebraMap K L) f).Splits → f.natDegree ∣ Module.finrank K L- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- MulZeroClass.mul_zeroproof · cited by 2,091
- Module.finrankstatement and proof · cited by 1,770
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- LT.lt.ne'proof · cited by 1,417
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.mapstatement and proof · cited by 806
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.natDegree_dvd_of_dvd_X_pow_card_pow_sub_Xproof · cited by 1