Proposition 2

a) Every quotient algebra of a $k$-algebra essentially of finite type is essentially of finite type.

b) Every ring of fractions of a $k$-algebra essentially of finite type is a $k$-algebra essentially of finite type.

c) The product $k$-algebra of a finite family of $k$-algebras essentially of finite type is essentially of finite type.

d) Let $k \to k'$ be a homomorphism of rings; for every $k$-algebra $A$ essentially of finite type, the $k'$-algebra $A_{(k')} = k' \otimes_k A$ is essentially of finite type.