In abstract algebra, an associative algebra A {\displaystyle A} over a ring R {\displaystyle R} is called finite if it is finitely generated as an R {\displaystyle R} -module. An R {\displaystyle R} -algebra can be thought as a homomorphism of rings f : R → A {\displaystyle f\colon R\to A} , in this case f {\displaystyle f} is called a finite morphism if A {\displaystyle A} is a finite R {\displaystyle R} -algebra.
In abstract algebra, an associative algebra A {\displaystyle A} over a ring R {\displaystyle R} is called finite if it is finitely generated as an R {\displaystyle R} -module. An R {\displaystyle R} -algebra can be thought as a homomorphism of rings f : R → A {\displaystyle f\colon R\to A} , in this case f {\displaystyle f} is called a finite morphism if A {\displaystyle A} is a finite R {\displaystyle R} -algebra.
Source: Wikipedia "Finite algebra" · CC BY-SA 4.0
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