Definition:Polynomial Algebra

Definition
Let $R$ be a ring.

Let $\Z \sqbrk X$ be the polynomial ring over the ring of integers $\Z$.

The polynomial algebra in one indeterminate over $R$ is the tensor product $R \otimes_\Z \Z \sqbrk X$.

Also see

 * Definition:Polynomial Ring
 * Definition:Tensor Product of R-Algebras