nLab étale algebra

Definition

An $R$-algebra $A$ is étale if the definition homomorphism $R \to A$ is, dually, an étale morphism of schemes.

A more elementary definition for algebras over a discrete field exists in constructive algebra.

Related concepts

étale morphism$\Rightarrow$ pro-étale morphism $\Rightarrow$ weakly étale morphism $\Rightarrow$ formally étale morphism

References

Henri Lombardi & Claude Quitté, Constructive Algebra, Constructive Methods, 2014, PDF