Given a commutative unit ring R and a filtration F:...⊆I_2 ⊆I_1 ⊆I_0 = R of ideals of R, the Rees ring of R with respect to F is R_+(F) = I_0 ⊕I_1 t⊕I_2 t^2 ⊕..., which is the set of all formal polynomials in the variable t in which the coefficient of t^i lies in I_i. It is a graded ring with respect to the usual addition and multiplication of polynomials, which makes it a subring of the polynomial ring R[t].

associated graded ring | Rees module