Saturation of a multiplicatively closed subset Exercise 3.7 of Atiyah-MacDonald asks the reader: if $A$ is a commutative ring and $\mathfrak{a} \triangleleft A$ an ideal, find the saturation of $1 + \mathfrak{a}$. Previously we have shown that the saturation of a multiplicatively closed subset $S$ is the complement of the union of prime ideals not meeting $S$. Are they just looking for the fact that the saturation is the complement of the union of all $\mathfrak{p}$ prime such that $\mathfrak{p} + \mathfrak{a} \neq R$? Or is there more to say?

You can say something more precise: $\overline S=A-\bigcup_{\mathfrak m\in\operatorname{Max}(A);\ \mathfrak a\subseteq\mathfrak m}\mathfrak m$.