Theorems · Theorem · field theory
minpolyDiv_ne_zero
∀ {R : Type u_2} {S : Type u_1} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {x : S},
IsIntegral R x → ∀ [Nontrivial S], minpolyDiv R x ≠ 0- Defined in
- Mathlib.FieldTheory.Minpoly.MinpolyDiv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cproof · cited by 1,598
- Polynomial.mapproof · cited by 806
- minpolyproof · cited by 439
- IsIntegralstatement and proof · cited by 427
Cited by2
Results whose statement or proof uses this declaration.
- natDegree_minpolyDiv_succproof · cited by 4
- minpolyDiv_monicproof · cited by 1