Set_of_Polynomials_over_Integral_Domain_is_Subring

Let $\struct {R, +, \circ}$ be a commutative ring. Let $\struct {D, +, \circ}$ be an integral subdomain of $R$. Then $\forall x \in R$, the set $D \sqbrk x$ of polynomials in $x$ over $D$ is a subring of $R$.