Unique_Representation_in_Polynomial_Forms

Let $\struct {R, +, \circ}$ be a commutative ring with unity whose zero is $0_R$ and whose unity is $1_R$. Let $\struct {D, +, \circ}$ be an integral subdomain of $R$. Let $X \in R$ be transcendental over $D$. Let $D \sqbrk X$ be the ring of polynomials in $X$ over $D$. Then each non-zero member of $D \left[{X}\right]$ can be expressed in just one way in the form $\ds f \in D \sqbrk X: f = \sum_{k \mathop = 0}^n {a_k \circ X^k}$