Theorems · Definition · commutative algebra
AdjoinRoot
{R : Type u_1} → [inst : CommRing R] → Polynomial R → Type u_1Adjoin a root of a polynomial f to a commutative ring R. We define the new ring
as the quotient of R[X] by the principal ideal generated by f.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 177 results in Mathlib
- Foundations
- Depth 93 from the axioms, rests on 2,367 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Polynomialstatement and proof · cited by 5,681
- HasQuotient.Quotientproof · cited by 2,301
- Ideal.spanproof · cited by 948
Cited by225
Results whose statement or proof uses this declaration.
- AdjoinRoot.rootstatement · cited by 77
- AdjoinRoot.ofstatement · cited by 52
- AdjoinRoot.mkstatement · cited by 50
- WeierstrassCurve.Affine.CoordinateRingproof · cited by 39
- AdjoinRoot.liftAlgHomstatement and proof · cited by 16
- AdjoinRoot.powerBasis'statement · cited by 12
- IsAdjoinRoot.adjoinRootAlgEquivstatement · cited by 11
- AdjoinRoot.liftstatement · cited by 11
- AdjoinRoot.aeval_eqstatement and proof · cited by 10
- AdjoinRoot.eval₂_rootstatement and proof · cited by 10
- AdjoinRoot.Minpoly.toAdjoinstatement · cited by 9
- AdjoinRoot.equiv'statement and proof · cited by 9
Showing the 200 most cited of 225.