I have started reading about graded rings and modules and filtered rings and modules. For grading at least,I can see the polynomials as a prototype,graded by usual degree. But I can't seem to find any motivation for filtration other than of course being abstract.
So I guess what I am looking for is :
- Some examples of filtration and related concepts that one might usually run into.
- Some theorems in algebra that require us to use filtration to prove them.