Theorems · Theorem · field theory
minpoly.degree_le
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Algebra A B] [Module.Finite A B] (x : B)
[Module.Free A B], (minpoly A x).degree ≤ ↑(Module.finrank A B)- Defined in
- Mathlib.FieldTheory.Minpoly.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Module.finrankstatement · cited by 1,770
- WithBotstatement · cited by 1,498
- Module.Finitestatement and proof · cited by 1,032
- Polynomial.degreestatement · cited by 643
- Module.Freestatement and proof · cited by 597
- minpolystatement · cited by 439
- Polynomial.degree_le_of_natDegree_leproof · cited by 10
- minpoly.natDegree_leproof · cited by 6
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