Theorems · Theorem · commutative algebra
MvPolynomial.ker_map
∀ {R : Type u} {S : Type u_1} {σ : Type v} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S),
RingHom.ker (MvPolynomial.map f) = Ideal.map MvPolynomial.C (RingHom.ker f)- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- Idealstatement · cited by 4,748
- MvPolynomialstatement and proof · cited by 2,140
- Ideal.mapstatement · cited by 692
- MvPolynomial.Cstatement · cited by 400
- RingHom.kerstatement and proof · cited by 363
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.mapstatement and proof · cited by 147
- Ideal.extproof · cited by 131
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.of_surjective_of_ker_eq_map_of_flatproof · cited by 1
- MvPolynomial.ker_mapAlgHomproof · cited by 0
- Algebra.FinitePresentation.mvPolynomial_of_finitePresentationproof · cited by 0