definition of product of modules I have been given this definition of a product between modules:
If $I$ is an indexing set with $M_i$ as an $R$-Module then the product
$\prod \limits_{i \in I} M_i$ is defined as the set consisting of I indexed tuples $(x_i)_{i\in I}$ for each $i \in I$ which is made into an R module by component wise addition and multiplication.
my problem is understanding this definition, could anyone give me a basic example of what the product of two Modules $M_1$ and $M_2$ would be, just so i could see how it works practically.
thanks in advance for the help!

Consider $\prod \limits_{i \in I} M_i$. 
The sum is $$( a_i)_{i \in I } + ( b_i)_{i \in I } = ( a_i + b_i)_{i \in I }$$  The action of R : $$ r \cdot ( a_i)_{i \in I } = ( r \cdot a_i)_{i \in I }$$
