Associated Graded Module

Question

I'm learning about Associated Graded Ring and Associated Graded Module. I got definition from Wiki:
My questions:

• What's $I^nM$?, it's mean: $I^nM=am, a\in I, m\in M$?
• With above define, so: $gr_I(M/xM)=?, gr_I(M/L)=?, x\in M,$ $L$ is a submodule of $M.$

Answer 1

• If $J\triangleleft R$, then $JM$ is the submodule of $M$ generated by elements of the form $am$ for $a\in J$ and $m\in M$

• If $I_1, I_2 \triangleleft R$, then $I_1I_2$ is the ideal generated by elements of the form $a_1a_2$ where $a_i\in I_i$.

Given $I\triangleleft R$, use $(b)$ to define $I^n$, and use $(a)$ to define $I^nM$