So I'm constructing an isomorphism and I need a general form of $\mathbb{Z}[X]/({X^2-m})$
I'm not too sure what this means, but I think it is a ideal of $\mathbb{Z}[X]$ generated by ${X^2-m}$? I can be completely wrong. Please clarify for me. Thank you
If $R$ is a ring and $r$ is an element of $R$, then the set $\{ar\mid a\in R\}$ is an ideal of $R$ (check this for yourself if it's not immediately obvious), and we typically denote this ideal by $(r)$ (or sometimes $\langle r\rangle$) and call it the ideal of $R$ generated by $r$.