In commutative algebra, given a homomorphism A → B {\displaystyle A\to B} of commutative rings, B {\displaystyle B} is called an A {\displaystyle A} -algebra of finite type if B {\displaystyle B} can be finitely generated as an A {\displaystyle A} -algebra. It is much stronger for B {\displaystyle B} to be a finite A {\displaystyle A} -algebra, which means that B {\displaystyle B} is finitely generated as an A {\displaystyle A} -module.
In commutative algebra, given a homomorphism A → B {\displaystyle A\to B} of commutative rings, B {\displaystyle B} is called an A {\displaystyle A} -algebra of finite type if B {\displaystyle B} can be finitely generated as an A {\displaystyle A} -algebra. It is much stronger for B {\displaystyle B} to be a finite A {\displaystyle A} -algebra, which means that B {\displaystyle B} is finitely generated as an A {\displaystyle A} -module.
Source: Wikipedia "Morphism of finite type" · CC BY-SA 4.0
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