Theorems · Theorem · commutative algebra
MvPolynomial.ker_mapAlgHom
∀ {R : Type u} [inst : CommRing R] {S₁ : Type u_2} {S₂ : Type u_3} {σ : Type u_4} [inst_1 : CommRing S₁]
[inst_2 : CommRing S₂] [inst_3 : Algebra R S₁] [inst_4 : Algebra R S₂] (f : S₁ →ₐ[R] S₂),
RingHom.ker (MvPolynomial.mapAlgHom f) = Ideal.map MvPolynomial.C (RingHom.ker f)- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- Idealstatement · cited by 4,748
- AlgHomstatement and proof · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- Ideal.mapstatement · cited by 692
- AlgHom.toRingHomproof · cited by 490
- MvPolynomial.Cstatement · cited by 400
- RingHom.kerstatement · cited by 363
- MvPolynomial.mapAlgHomstatement · cited by 15
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