For an ideal , the Rees ring is the graded subringIt packages all powers of into one algebra and turns stable filtrations into finitely generated graded modules.
The Rees module of an -module with respect to an ideal is , a graded module over the Rees ring . Generators of in degree zero generate this module. For , the graded submodule is finitely generated when is a Noetherian ring; a bound on its generators' degrees yields the Artin-Rees lemma.
Articles by others on the same topic
Rees algebra is a construction in commutative algebra that generalizes the notion of an ideal in a ring. It is particularly useful in the study of local rings and algebraic geometry. The Rees algebra is named after David Rees, who introduced it as a tool for the study of properties of ideals and their associated varieties.