I am trying to do an assignment question, but I'm struggling with notation. It is described in the question, but I can't quite visualise what it means - and it seems as though it's really straightforward!
Let $R$ be a ring, $I\subset R$ a nilpotent ideal and $E$ a simple $R$-module.
I am required to do something with the set $IE$. I know what I need to do, but I do not know what $IE$ means.
Intuitively, I would assume $$IE=\{ax\mid a\in I, x\in E\}.$$
However, in the question, it is described as follows:
"where $IE$ is the set of all sums of elements $ax$ with $a\in I$ and $x\in E$."
Which is making me think that $IE$ is the following (I'm not sure of the correct notation here...) $$IE=\left\{\sum ax \mid a\in I, x\in E\right\}.$$
I am trying to prove that this set is a submodule of $E$ - which I am perfectly comfortable with doing and do not need any help with. But I need to know exactly the set I need to check!
Thanks,
Andy.