Hi!

I have problem with this exercice

Find three ideals $\displaystyle (a)$ in $\displaystyle \in{\mathbb{Z}} $ with thr property that $\displaystyle (24)\subsetneq (a) $ ($\displaystyle \subsetneq$ means is a proper subsets of)

- Definition

An ideal in a commutative ring $\displaystyle R$ is a subset $\displaystyle I$ of $\displaystyle R$ such that

$\displaystyle a)$ $\displaystyle 0\in{I}$

$\displaystyle b)$ $\displaystyle a,b \in{I} \Rightarrow{a+b \in{I}} $

$\displaystyle c)$ If $\displaystyle a\in{I}$, $\displaystyle r\in{A}$ then$\displaystyle ra \in{I}$

I think of $\displaystyle (2)$ $\displaystyle (4)$ and $\displaystyle (6)$ but are not ideal since $\displaystyle (b)$fails