Theorems · Definition · commutative algebra
AdjoinRoot.lift
{R : Type u_1} →
{S : Type u_2} →
[inst : CommRing R] →
{f : Polynomial R} →
[inst_1 : CommRing S] → (i : R →+* S) → (x : S) → Polynomial.eval₂ i x f = 0 → AdjoinRoot f →+* SLift a ring homomorphism i : R →+* S to AdjoinRoot f →+* S.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Ideal.spanproof · cited by 948
- Polynomial.eval₂statement and proof · cited by 267
- AdjoinRootstatement · cited by 177
- Ideal.Quotient.liftproof · cited by 19
- Polynomial.eval₂RingHomproof · cited by 19
Cited by15
Results whose statement or proof uses this declaration.
- AdjoinRoot.liftAlgHomproof · cited by 16
- AdjoinRoot.mapproof · cited by 8
- AdjoinRoot.lift_mkstatement · cited by 6
- AdjoinRoot.lift_rootstatement and proof · cited by 6
- AdjoinRoot.lift_ofstatement and proof · cited by 5
- AdjoinRoot.minpoly_rootproof · cited by 3
- WeierstrassCurve.Affine.CoordinateRing.mapproof · cited by 3
- AdjoinRoot.evalEvalproof · cited by 2
- Algebra.IsStandardEtale.of_isLocalizationAwayproof · cited by 2
- StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_xproof · cited by 1
- AdjoinRoot.lift_comp_ofstatement · cited by 0
- mem_adjoin_map_integralClosure_of_isStandardEtaleproof · cited by 0