# Construction of graded rings and modules

In Algebraic Geometry and Homological Algebra - as far as I know - we often consider graded rings and modules so as to encode more information, say, some sort of (computational) complexity. For example, the powers of an ideal give rise to a filtration on the ring (and also on a module over that ring), which finally provides us with the associated graded ring (respectively, module), having important geometric attributes.

I am just wondering whether there are any less common methods (of course, beyond the standard) to obtain graded algebraic structures.

EDIT: Perhaps I omitted some details. Here they are.

I am currently working on the resolution of singular algebraic varieties, and I have just come up with the idea of somehow measuring the badness of singularities in terms of the Castelnuovo--Mumford regularity. Thus, I need graded structures where the degrees encode important information about the singular behaviour. Since we work with polynomial algebras, we have standard techniques (e.g. weights associated to the generators, or the one I described above), however, even in the case of hypersurfaces, they are of no interest. Hence, I am curious about other methods that, given a ring (or a module), result in a graded ring (respectively, module) having some similarities with the original one.

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Which ones are the standard ones? – Qiaochu Yuan Aug 10 '12 at 17:35
I'm about to mention two common methods because I just have no way of knowing if you are aware of them. Semigroup rings are naturally (semigroup) graded, and real Clifford algebras have a kind of grading that makes them amenable for some geometric applications. (The grading is defined for other fields too but I can't speak to their uses.) – rschwieb Aug 10 '12 at 18:31
By standard I mean standard (possibly multi-) graded polynomial algebras. I am also aware of Rees algebras, but they still rely heavily upon an ideal of a ring. I would be glad to hear about other approaches. – Norbert Pintye Aug 10 '12 at 18:44