Theorems · Definition · algebraic geometry
WeierstrassCurve.Affine.CoordinateRing.map
{R : Type r} →
{S : Type s} →
[inst : CommRing R] →
[inst_1 : CommRing S] →
(W' : WeierstrassCurve.Affine R) → (f : R →+* S) → W'.CoordinateRing →+* (W'.map f).CoordinateRingThe ring homomorphism R[W] →+* S[W.map f] induced by a ring homomorphism f : R →+* S.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 5,681
- RingHom.compproof · cited by 899
- WeierstrassCurve.Affinestatement and proof · cited by 174
- Polynomial.mapRingHomproof · cited by 98
- AdjoinRoot.rootproof · cited by 77
- WeierstrassCurve.Affine.polynomialstatement and proof · cited by 61
- AdjoinRoot.ofproof · cited by 52
- WeierstrassCurve.Affine.CoordinateRingstatement · cited by 39
- WeierstrassCurve.Affine.mapstatement and proof · cited by 20
- AdjoinRoot.liftproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.CoordinateRing.map_mkstatement · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.map_smulstatement and proof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.map_injectivestatement and proof · cited by 0