Theorems · Theorem · commutative algebra
AdjoinRoot.powerBasis_gen
∀ {K : Type u_5} [inst : Field K] {f : Polynomial K} (hf : f ≠ 0), (AdjoinRoot.powerBasis hf).gen = AdjoinRoot.root f- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- AdjoinRootstatement · cited by 177
- PowerBasis.genstatement and proof · cited by 122
- AdjoinRoot.rootstatement · cited by 77
- AdjoinRoot.powerBasisstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- AdjoinRoot.minpoly_powerBasis_genproof · cited by 1