Theorems · Definition · commutative algebra
AdjoinRoot.mk
{R : Type u_1} → [inst : CommRing R] → (f : Polynomial R) → Polynomial R →+* AdjoinRoot fRing homomorphism from R[x] to AdjoinRoot f sending X to the root.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Ideal.spanproof · cited by 948
- Ideal.Quotient.mkproof · cited by 610
- AdjoinRootstatement · cited by 177
Cited by59
Results whose statement or proof uses this declaration.
- AdjoinRoot.rootproof · cited by 77
- AdjoinRoot.ofproof · cited by 52
- WeierstrassCurve.Affine.CoordinateRing.mkproof · cited by 25
- AdjoinRoot.aeval_eqstatement and proof · cited by 10
- AdjoinRoot.mk_selfstatement · cited by 8
- AdjoinRoot.mk_surjectivestatement · cited by 7
- AdjoinRoot.lift_mkstatement · cited by 6
- AdjoinRoot.mk_eq_mkstatement · cited by 6
- AdjoinRoot.quotMapOfEquivQuotMapCMapMkstatement · cited by 5
- AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapMkstatement · cited by 5
- AdjoinRoot.mk_eq_zerostatement · cited by 4
- AdjoinRoot.mk_ne_zero_of_natDegree_ltstatement · cited by 4