Is there a formal way to define $\mathbf{R}(X^n)$

Question

For example $\mathbf{C}$ or $\mathbf{R}[i]$ can be defined as $\mathbf{R}[X]/(X^2+1)$ but this is to "extend" $\mathbf{R}$.

Is there a "similar" way to define $\mathbf{R}(X^n)$ ?

Thanks