Polynomial ring

Definition for commutative rings

Definition with symbols

Let $R$ denote a commutative unital ring. The, the polynomial ring over $R$ in one variable, denoted as $R[x]$ where $x$ is termed the indeterminate, is defined as the ring of formal polynomials in $x$ with coefficients on $R$.

Functoriality

The map sending a commutative unital ring to its polynomial ring is a self-functor on the category of commutative unital rings.