**Finitely-generated Algebra**

In mathematics, a **finitely generated algebra** is an associative algebra *A* over a field *K* where there exists a finite set of elements *a*_{1},…,*a*_{n} of *A* such that every element of *A* can be expressed as a polynomial in *a*_{1},…,*a*_{n}, with coefficients in *K*. If it is necessary to emphasize the field *K* then the algebra is said to be finitely generated **over K** . Algebras that are not finitely generated are called

**infinitely generated**. Finitely generated commutative algebras are basic objects of consideration in modern algebraic geometry, where they correspond to affine algebraic varieties; for this reason, these algebras are also referred to as (commutative)

**affine algebras**.

Read more about Finitely-generated Algebra: Examples, Properties

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