Theorems · Definition · commutative algebra

AlgHom.Finite

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : CommRing A] →
          [inst_2 : CommRing B] → [inst_3 : Algebra R A] → [inst_4 : Algebra R B] → (A →ₐ[R] B) → Prop

An algebra morphism A →ₐ[R] B is finite if it is finite as ring morphism. In other words, if B is finitely generated as A-module.

Defined in

Mathlib.RingTheory.Finiteness.Defs

Cited by

11 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebra