Why $R/AB$ is cyclic when $A,B$ are ideals of $R$?
I know a cyclic module is a module that can be written as $Rm$ and $Rm$ is isomorphic to $R/Ann(m)$. However, I can't see why the module is cyclic, unless AB is an annihilator of something. Can someone explain to me please?
A cyclic module is a module, that is generated by one element. For sure $R/AB$ is generated by the class of $1$.
$AB$ is precisely the annihilator of $\overline 1 = 1+AB \in R/AB$.