Theorems · Definition · commutative algebra
IsAdjoinRootMonic.powerBasis
{R : Type u} →
{S : Type v} →
[inst : CommRing R] →
[inst_1 : Ring S] → {f : Polynomial R} → [inst_2 : Algebra R S] → IsAdjoinRootMonic S f → PowerBasis R SIf f is monic, the powers of h.root form a basis.
- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreeproof · cited by 1,105
- PowerBasisstatement · cited by 115
- IsAdjoinRootMonicstatement and proof · cited by 35
- IsAdjoinRoot.rootproof · cited by 34
- IsAdjoinRootMonic.toIsAdjoinRootproof · cited by 18
- IsAdjoinRootMonic.basisproof · cited by 10
- IsAdjoinRootMonic.basis_applyproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- IsAdjoinRootMonic.finrankproof · cited by 2
- IsAdjoinRootMonic.powerBasis_basisstatement and proof · cited by 0
- IsAdjoinRootMonic.powerBasis_dimstatement and proof · cited by 0
- IsAdjoinRootMonic.powerBasis_genstatement and proof · cited by 0
- IsAdjoinRootMonic.finiteproof · cited by 0