Theorems · Definition · commutative algebra

PowerBasis.ofAdjoinEqTop

{K : Type u_1} →
  {S : Type u_2} →
    [inst : Field K] →
      [inst_1 : CommRing S] → [inst_2 : Algebra K S] → {x : S} → IsIntegral K x → K[x] = ⊤ → PowerBasis K S

If x generates S over K and is integral over K, then it defines a power basis. See PowerBasis.ofAdjoinEqTop' for a version over a more general base ring.

Defined in

Mathlib.RingTheory.Adjoin.PowerBasis

Cited by

2 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCommRingAlgebra