For a commutative ring R with unity and element x $\in$ R:
Consider the principal ideal $\left \langle x \right \rangle$
This is just $\left \langle x \right \rangle = \left \{ rx:r \in R \right \}$
In general, what are the form of the elements in $\left \langle n,x \right \rangle $, say, for any integer n? I can't quite remember coming across this particular set/ notation in any literatures or text.
A list of elements of a ring surrounded by angle brackets (or parens) is common notation for the ideal generated by the set of those elements. It is an abbreviation from writing the set with braces within brackets or parens.
It's easy to verify that the ideal generated by $x$ and $y$ is $\{xr +ys\mid r,s\in R\}$.