Theorems · Definition · commutative algebra

Algebra.Generators.Hom.toAlgHom

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : Algebra R S] →
            {P : Algebra.Generators R S ι} →
              {R' : Type u_1} →
                {S' : Type u_2} →
                  {ι' : Type u_3} →
                    [inst_3 : CommRing R'] →
                      [inst_4 : CommRing S'] →
                        [inst_5 : Algebra R' S'] →
                          {P' : Algebra.Generators R' S' ι'} →
                            [inst_6 : Algebra R R'] → [inst_7 : Algebra S S'] → P.Hom P' → P.Ring →ₐ[R] P'.Ring

A hom between two families of generators gives an algebra homomorphism between the polynomial rings.

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

30 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebra