Theorems · Theorem · commutative algebra
Algebra.adjoin.powerBasis_dim
∀ {K : Type u_1} {S : Type u_2} [inst : Field K] [inst_1 : CommRing S] [inst_2 : Algebra K S] {x : S}
(hx : IsIntegral K x), (Algebra.adjoin.powerBasis hx).dim = (minpoly K x).natDegree- Defined in
- Mathlib.RingTheory.Adjoin.PowerBasis
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 125 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.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subalgebrastatement · cited by 1,353
- Polynomial.natDegreestatement · cited by 1,105
- Algebra.adjoinstatement · cited by 535
- minpolystatement · cited by 439
- IsIntegralstatement and proof · cited by 427
- PowerBasis.dimstatement and proof · cited by 74
- Algebra.adjoin.powerBasisstatement and proof · cited by 2
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