Suppose that $a$ and $b$ belong to an integral domain, $b\neq 0$, and $a$ is not a unit. Show that $\langle ab\rangle$ is a proper subset of $\langle b\rangle$.
How can I solve this problem?
Suppose that $a$ and $b$ belong to an integral domain, $b\neq 0$, and $a$ is not a unit. Show that $\langle ab\rangle$ is a proper subset of $\langle b\rangle$.
How can I solve this problem?