Hi,
what comes to the mind of a physicist, when he hears words like filtered ring and associated graded? What do these guys describe? What are basic/typical/illuminating examples in physics? 
Of course also mathematicians may answer from their perspective :)

Edit: Information on my background: My "primeval" motivation to understand filtered rings/graded rings, comes from mathematics: They are the basics for D-Module theory. 
Though I would also like to see these rings from a different perspective, therefor I asked the question.
 My knowledge in physics is a bit limited, I only attended some undergraduate courses (quantum mechanics, electro dynamics, classical mechanics). Though more sophisticated answers are fine, I don't need to understand every detail, I just want to get the flavor.