Polynomial Rings

Let $A$ be a ring. A univariate polynomial $P$ over $A$ is formally defined as a sequence $\mu :\mathbb{N}\to A$ with finite support. Then the value at a point $x:A$ is given by, $P_{\mu }(x)={\sum }_{i=0}^{\infty }\mu (i)x^i$

Because $\mu$ has finite support, this sum is always well-defined in $A[x]$.