Theorems · Definition · commutative algebra

Algebra.adjoin.powerBasis

{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 → PowerBasis K ↥K[x]

The power basis 1, x, ..., x ^ (d - 1) for K[x], where d is the degree of the minimal polynomial of x. See Algebra.adjoin.powerBasis' for a version over a more general base ring.

Defined in

Mathlib.RingTheory.Adjoin.PowerBasis

Cited by

2 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCommRingAlgebra