Finite algebra

In abstract algebra, an associative algebra

is called finite if it is finitely generated as an

-algebra can be thought as a homomorphism of rings

is called a finite morphism if

[1] Being a finite algebra is a stronger condition than being an algebra of finite type.

This concept is closely related to that of finite morphism in algebraic geometry; in the simplest case of affine varieties, given two affine varieties

and a dominant regular map

, the induced homomorphism of

-algebra: The generalisation to schemes can be found in the article on finite morphisms.

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